Advertisements
Advertisements
рдкреНрд░рд╢реНрди
Find the consecutive even integers whose squares have the sum 340.
Advertisements
рдЙрддреНрддрд░
Let the consecutive even integers be 2x and 2x + 2.
Then according to the given hypothesis,
(2ЁЭСе)2 + (2ЁЭСе + 2)2 = 340
⇒ 8ЁЭСе2 + 8ЁЭСе - 336 = 0
⇒ ЁЭСе2 + ЁЭСе - 42 = 0
⇒ ЁЭСе2 + 7ЁЭСе - 6ЁЭСе - 42 = 0
⇒ ЁЭСе(ЁЭСе + 7) - 6(ЁЭСе + 7) = 0
⇒ (ЁЭСе + 7)(ЁЭСе - 6) = 0
⇒ x = -7 or x = 6
Considering, the positive integers of x.
⇒ x = 6; 2x = 12 and 2x + 2 = 14.
∴ The two consecutive even integers are 12 and 14.
APPEARS IN
рд╕рдВрдмрдВрдзрд┐рдд рдкреНрд░рд╢реНрди
Solve for x
`(2x)/(x-3)+1/(2x+3)+(3x+9)/((x-3)(2x+3)) = 0, x!=3,`
Find x in terms of a, b and c: `a/(x-a)+b/(x-b)=(2c)/(x-c)`
Find the roots of the following quadratic equation by factorisation:
`sqrt2 x^2 +7x+ 5sqrt2 = 0`
Solve the following quadratic equations by factorization:
`a/(x-a)+b/(x-b)=(2c)/(x-c)`
A passenger train takes 3 hours less for a journey of 360 km, if its speed is increased by 10 km/hr from its usual speed. What is the usual speed?
A takes 10 days less than the time taken by B to finish a piece of work. If both A and B together can finish the work in 12 days, find the time taken by B to finish the work.
Without solving the following quadratic equation Find the value of p for which the roots are equal
`px^2 - 4x + 3 = 0`
Find the values of k for which the roots are real and equal in each of the following equation:\[px(x - 3) + 9 = 0\]
The value of c for which the equation ax2 + 2bx + c = 0 has equal roots is
Solve the following equation :
`("x" - 1)/("x" - 2) + ("x" - 3)/("x" - 4) = 3 1/3`
The product of a girl's age five years ago and her age 3 years later is 105. Find her present age.
Some students planned a picnic. The budget for the food was Rs. 480. As eight of them failed to join the party, the cost of the food for each member increased by Rs. 10. Find how many students went for the picnic.
Solve the following by reducing them to quadratic equations:
`((7y - 1)/y)^2 - 3 ((7y - 1)/y) - 18 = 0, y ≠ 0`
If x = p is a solution of the equation x(2x + 5) = 3, then find the value of p.
Solve the following equation by factorisation :
2x2 + ax – a2= 0
Forty years hence, Mr. Pratap’s age will be the square of what it was 32 years ago. Find his present age.
Solve the quadratic equation by factorisation method:
x2 – 15x + 54 = 0
A dealer sells a toy for тВ╣ 24 and gains as much percent as the cost price of the toy. Find the cost price of the toy.
Complete the following activity to solve the given quadratic equation by factorization method.
Activity: x2 + 8x – 20 = 0
x2 + ( __ ) – 2x – 20 = 0
x (x + 10) – ( __ ) (x + 10) = 0
(x + 10) ( ____ ) = 0
x = ___ or x = 2
Find a natural number whose square diminished by 84 is equal to thrice of 8 more than the given number.
