Advertisements
Advertisements
प्रश्न
Divide 29 into two parts so that the sum of the square of the parts is 425.
उत्तर
Let the parts be x and 29 - x
According to the problem
x2 + (29 - x)2 = 425
⇒ x2 + 841 + x2 - 58x - 425 = 0
⇒ 2x2 - 58x + 416 = 0
⇒ x2 - 29x + 208 = 0
⇒ x2 - 16x - 13x + 208 = 0
⇒ x(x - 16) - 13(x - 16) = 0
⇒ (x - 16) (x - 13) = 0
⇒ x - 16 = 0 or x - 13 = 0
⇒ x = 16 or x = 13
When x = 16 When x = 13
Then 29 - x = 13 Then 29 - x = 16
Hence, the parts are 16 and 13.
APPEARS IN
संबंधित प्रश्न
Solve the following quadratic equations by factorization:
3x2 = -11x - 10
Solve the following quadratic equations by factorization:
`(x-a)/(x-b)+(x-b)/(x-a)=a/b+b/a`
Solve the following quadratic equations by factorization: \[2 x^2 + ax - a^2 = 0\]
Solve the following quadratic equations by factorization: \[\frac{x - 4}{x - 5} + \frac{x - 6}{x - 7} = \frac{10}{3}; x \neq 5, 7\]
In the following determine the set of values of k for which the given quadratic equation has real roots: \[2 x^2 + x + k = 0\]
A quadratic equation whose one root is 2 and the sum of whose roots is zero, is ______.
Solve the following : `("x" - 1/2)^2 = 4`
Three years ago, a man was 5 times the age of his son. Four years hence, he will be thrice his son's age. Find the present ages of the man and his son.
In each of the following determine whether the given values are solutions of the equation or not.
x2 + `sqrt(2)` - 4 = 0; x = `sqrt(2)`, x = -2`sqrt(2)`
Solve the following equation by factorization
`x^2 - (1 + sqrt(2))x + sqrt(2)` = 0
