If A2 + B2 + C2 = 20 and a + B + C = 0, Find Ab + Bc + Ca. - Mathematics

Advertisements
Advertisements
Answer in Brief

If a2 + b2 + c2 = 20 and a + b + c = 0, find ab + bc + ca.

Advertisements

Solution

Recall the formula

 `(a+b+c)^2 = a^+b^2 +c^2 +2(ab +bc +ca)`

Given that

`a^2 +b^2 +c^2 = 20`

`(a+b+c) = 0`

Then we have

                 `(a+b+c)^2 = a^2 +b^2 +c^2 +2 (ab +bc + ca)`

                                `(0)^2 = 20 +2(ab +bc + ca)`

  ` 20+2(ab +bc + ca) = 0`

            `2(ab + bc + ca) = -20`

               `(ab +bc + ca) = -10`

  Is there an error in this question or solution?
Chapter 5: Factorisation of Algebraic Expressions - Exercise 5.5 [Page 24]

APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 5 Factorisation of Algebraic Expressions
Exercise 5.5 | Q 2 | Page 24

RELATED QUESTIONS

Get the algebraic expression in the following case using variables, constants and arithmetic operations.

One-half of the sum of numbers x and y.


Factorize: x3 + x - 3x2 - 3


Factorize x2 - y2 - 4xz + 4z2


Factorize `2x^2 - 5/6x + 1/12`


Factorize the following expressions:

y3 +125


Factorize the following expressions:

1029 – 3x3


Factorize the following expressions:

8a3 - b3 - 4ax + 2bx


Factorize  x3  -12x ( x - 4) - 64


125 + 8x3 - 27 y3 + 90xy


`2sqrt2a^3 + 3sqrt3b^3 + c^3 - 3 sqrt6abc`


If \[x^2 + \frac{1}{x^2} = 18,\]  find the values of \[x + \frac{1}{x} \text { and } x - \frac{1}{x} .\]


If x + y = 4 and xy = 2, find the value of x2 + y2


If 3x + 5y = 11 and xy = 2, find the value of 9x2 + 25y2


Find the value of the following expression: 16x2 + 24x + 9, when \[x = \frac{7}{4}\]


Find the value of the following expression:  64x2 + 81y2 + 144xy, when x = 11 and \[y = \frac{4}{3}\]


What must be added to the following expression to make it a whole square? 

4x2 − 12x + 7


What must be added to the following expression to make it a whole square? 

4x2 − 20x + 20


If (x + y)3 − (x − y)3 − 6y(x2 − y2) = ky2, then k =


Separate the constants and variables from the following :

`-7,7+"x",7"x"+"yz",sqrt5,sqrt("xy"),(3"yz")/8,4.5"y"-3"x",`

8 −5, 8 − 5x, 8x −5y × p and 3y2z ÷ 4x


Write the number of the term of the following polynomial.

5x2 + 3 x ax


Write the number of the term of the following polynomial.

ax ÷ 4 – 7


Write the number of the term of the following polynomial.

ax – by + y x z


Write the number of the term of the following polynomial.

23 + a x b ÷ 2


Separate monomials, binomials, trinomials and polynomials from the following algebraic expressions :

8 − 3x, xy2, 3y2 − 5y + 8, 9x − 3x2 + 15x3 − 7,
3x × 5y, 3x ÷ 5y, 2y ÷ 7 + 3x − 7 and 4 − ax2 + bx + y


Evaluate: (3c - 5d)(4c - 6d)


Evaluate: (4m - 2)(m2 + 5m - 6) 


Multiply: (2x + 3y)(2x + 3y)


Multiply: (2x + 3y)(2x - 3y)


Multiply: (x - a)(x + 3b)


Multiply: (3x - 5y + 2)(5x - 4y - 3)


Divide: n2 - 2n + 1 by n - 1 


The area of a rectangle is 6x2 – 4xy – 10y2 square unit and its length is 2x + 2y unit. Find its breadth.


Divide: x5 - 15x4 - 10x2 by -5x2 


Divide: x3 - 6x2 + 11x - 6 by x2 - 4x + 3 


Write in the form of an algebraic expression:

Perimeter (P) of a rectangle is two times the sum of its length (l) and its breadth (b).


Write in the form of an algebraic expression:

Perimeter (P) of a square is four times its side.


Write in the form of an algebraic expression:

Area of a square is square of its side.


Write in the form of an algebraic expression:

Surface area of a cube is six times the square of its edge.


Express the following as an algebraic expression:

The product of x and y divided by m.


Express the following as an algebraic expression:

The subtraction of 5m from 3n and then adding 9p to it.


Express the following as an algebraic expression:

The product of 12, x, y and z minus the product of 5, m and n.


Express the following as an algebraic expression:

Sum of p and 2r – s minus sum of a and 3n + 4x.


Construct a formula for the following:

Total wages (₹ W) of a man whose basic wage is (₹ B) for t hours week plus (₹ R) per hour, if he Works a total of T hours.


Find the average (A) of four quantities p, q, r and s. If A = 6, p = 3, q = 5 and r = 7; find the value of s.


Solve the following equation.

4(​x + 12) = 8 


Solve the following equation.

3y + 4 = 5y - 6


Choose the right answer from the option.

The simplest form of 5 ÷ `(3/2) - 1/3` is _______.


Choose the right answer from the option.

The solution of the equation `"3x" - 1/2 = 5/2 + "x"` is _____.


Choose the right answer from the option.

Which of the following expressions has the value 37?


Write the coefficient of x2 and x in the following polynomials

`4 + 2/5x^2 - 3x`


Write the coefficient of x2 and x in the following polynomials

`6 - 2x^2 + 3x^3 - sqrt(7)x`


Write the coefficient of x2 and x in the following polynomials

πx2 – x + 2


Write the coefficient of x2 and x in the following polynomials

`sqrt(3)x^2 + sqrt(2)x + 0.5`


Write the coefficient of x2 and x in the following polynomials

`x^2 - 7/2 x + 8`


Complete the table.

× 2x2 −2xy x4y3 2xyz (___)xz2
x4          
(___)     4x5y4    
−x2y          
2y2z         −10xy2z3
−3xyz          
(___)       −14xyz2  

The largest number of the three consecutive numbers is x + 1, then the smallest number is ________


The variable in the expression 16x – 7 is __________


The constant term of the expression 2y – 6 is _________


When y = –1, the value of the expression 2y – 1 is 3


Write the variables, constant and terms of the following expression

18 + x – y


Write the variables, constant and terms of the following expression

7p – 4q + 5


Write the variables, constant and terms of the following expression

b + 2


If x = 2 and y = 3, then find the value of the following expressions

2x – 3y


If x = 2 and y = 3, then find the value of the following expressions

x + y


If x = 2 and y = 3, then find the value of the following expressions

4y – x


If x = 2 and y = 3, then find the value of the following expressions

x + 1 – y


An algebraic statement which is equivalent to the verbal statement “Three times the sum of ‘x’ and ‘y’ is


The value of 7a – 4b when a = 3, b = 2 is


Give an algebraic equation for the following statement:

“The difference between the area and perimeter of a rectangle is 20”.


In a polynomial, the exponents of the variables are always ______.


Which of the following is correct?


Number of terms in the expression a2 + bc × d is ______.


In the expression 2πr, the algebraic variable is ______.


The total number of planets of Sun can be denoted by the variable n.


Shiv works in a mall and gets paid ₹ 50 per hour. Last week he worked for 7 hours and this week he will work for x hours. Write an algebraic expression for the money paid to him for both the weeks.


A school has a rectangular playground with length x and breadth y and a square lawn with side x as shown in the figure given below. What is the total perimeter of both of them combined together?


The rate of planting the grass is ₹ x per square metre. Find the cost of planting the grass on a triangular lawn whose base is y metres and height is z metres.


Rohan's mother gave him ₹ 3xy2 and his father gave him  ₹ 5(xy2 + 2). Out of this total money he spent ₹ (10 – 3xy2) on his birthday party. How much money is left with him?


A triangle is made up of 2 red sticks and 1 blue sticks . The length of a red stick is given by r and that of a blue stick is given by b. Using this information, write an expression for the total length of sticks in the pattern given below:


Express the following properties with variables x, y and z.

Commutative property of addition


Express the following properties with variables x, y and z.

Associative property of addition


Share
Notifications



      Forgot password?
Use app×