Advertisements
Advertisements
рдкреНрд░рд╢реНрди
The sum of two numbers is 8 and 15 times the sum of their reciprocals is also 8. Find the numbers.
Advertisements
рдЙрддреНрддрд░
Let the numbers be x and 8 − x
Given that the sum of these numbers is 8
And 15 times the sum of their reciprocals as 8
`rArr15(1/x+1/(8-x))=8`
`rArr15(((8-x)+x)/(x(8-x)))=8`
⇒ 15 ((8 − ЁЭСе) + ЁЭСе) = 8(ЁЭСе(8 − ЁЭСе))
⇒ 15 [8 − ЁЭСе + ЁЭСе] = 8ЁЭСе(8 − ЁЭСе)
⇒ 120 = 64x − 8x2
⇒ 8ЁЭСе2 − 64ЁЭСе + 120 = 0
⇒ 8[ЁЭСе2 − 8ЁЭСе + 15] = 0
⇒ ЁЭСе2 − 5ЁЭСе − 3ЁЭСе + 15 = 0
⇒ (ЁЭСе − 5) (ЁЭСе − 3) = 0
⇒ x = 5 or x = 3
∴ The two numbers are 5 and 3.
рд╕рдВрдмрдВрдзрд┐рдд рдкреНрд░рд╢реНтАНрди
Solve the following quadratic equation for x: x2 – 2ax – (4b2 – a2) = 0
Solve for x :
`2/(x+1)+3/(2(x-2))=23/(5x), x!=0,-1,2`
A cottage industry produces a certain number of toys in a day. The cost of production of each toy (in rupees) was found to be 55 minus the number of toys produced in a day. On a particular day, the total cost of production was Rs 750. We would like to find out the number of toys produced on that day.
Solve the following quadratic equations by factorization:
`2/2^2-5/x+2=0`
Solve the following quadratic equations by factorization:
a2x2 - 3abx + 2b2 = 0
Solve the following quadratic equations by factorization:
4x2 + 4bx - (a2 - b2) = 0
A two digits number is such that the product of the digits is 12. When 36 is added to the number, the digits inter change their places determine the number.
The difference of squares of two number is 88. If the larger number is 5 less than twice the smaller number, then find the two numbers.
Solve : x2 – 11x – 12 =0; when x ∈ N
`3x^2-x-2=0`
The sum of two natural number is 28 and their product is 192. Find the numbers.
The sum of the squares of two consecutive positive even numbers is 452. Find the numbers.
Solve the following quadratic equation by factorization: \[\frac{a}{x - b} + \frac{b}{x - a} = 2\]
Find the values of k for which the roots are real and equal in each of the following equation:
\[4 x^2 - 2\left( k + 1 \right)x + \left( k + 1 \right) = 0\]
Find the values of k for which the quadratic equation
\[\left( 3k + 1 \right) x^2 + 2\left( k + 1 \right)x + 1 = 0\] has equal roots. Also, find the roots.
If the equation 9x2 + 6kx + 4 = 0 has equal roots, then the roots are both equal to
If the equation ax2 + 2x + a = 0 has two distinct roots, if
Solve the following equation :
`sqrt 2 "x"^2 - 3"x" - 2 sqrt 2 = 0`
Solve the following equation : `"ax"^2 + (4"a"^2 - 3"b")"x" - 12"ab" = 0`
The perimeter of the right angled triangle is 60cm. Its hypotenuse is 25cm. Find the area of the triangle.
If an integer is added to its square the sum is 90. Find the integer with the help of a quadratic equation.
By increasing the speed of a car by 10 km/hr, the time of journey for a distance of 72 km. is reduced by 36 minutes. Find the original speed of the car.
Solve the following by reducing them to quadratic form:
`sqrt(y + 1) + sqrt(2y - 5) = 3, y ∈ "R".`
In each of the following, determine whether the given values are solution of the given equation or not:
x2 + x + 1 = 0; x = 0; x = 1
Find the values of x if p + 7 = 0, q – 12 = 0 and x2 + px + q = 0,
The difference between the squares of two numbers is 45. The square of the smaller number is 4 times the larger number. Determine the numbers.
The length of a rectangle exceeds its breadth by 5 m. If the breadth were doubled and the length reduced by 9 m, the area of the rectangle would have increased by 140 m². Find its dimensions.
The perimeter of a rectangular plot is 180 m and its area is 1800 m2. Take the length of the plot as x m. Use the perimeter 180 m to write the value of the breadth in terms of x. Use the values of length, breadth and the area to write an equation in x. Solve the equation to calculate the length and breadth of the plot.
By selling an article for Rs. 21, a trader loses as much per cent as the cost price of the article. Find the cost price.
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.
