The sum of two numbers is 17 and the sum of their squares is 157 . Find the number.

Question

The sum of two numbers is 17 and the sum of their squares is 157 . Find the number. (A) 9 (B) 6 (C) 11 (D) None of these

Tardigrade Admin · Accepted Answer

Let the numbers be x and (17-x) According to the given information, x2+(17-x)2 =157 x2+289+x2-34 x =157 2 x2-34 x+132 =0 x2-17 x+66 =0 x2-11 x-6 x+66 =0 x(x-11)-6(x-11) =0 (x-11)(x-6) =0 x =11,6

Q. The sum of two numbers is 17 and the sum of their squares is 157 . Find the number.

9

6

11

None of these

Let the numbers be $x$ and $(17 - x)$
According to the given information,
$x^{2} + (17 - x)^{2} = 157$
$x^{2} + 289 + x^{2} - 34 x = 157$
$2 x^{2} - 34 x + 132 = 0$
$x^{2} - 17 x + 66 = 0$
$x^{2} - 11 x - 6 x + 66 = 0$
$x (x - 11) - 6 (x - 11) = 0$
$(x - 11) (x - 6) = 0$
$x = 11, 6$

Q. The sum of two numbers is 17 and the sum of their squares is 157 . Find the number.

9

6

11

None of these

Let the numbers be x and (17−x) According to the given information, x2+(17−x)2=157 x2+289+x2−34x=157 2x2−34x+132=0 x2−17x+66=0 x2−11x−6x+66=0 x(x−11)−6(x−11)=0 (x−11)(x−6)=0 x=11,6

Let the numbers be $x$ and $(17 - x)$
According to the given information,
$x^{2} + (17 - x)^{2} = 157$
$x^{2} + 289 + x^{2} - 34 x = 157$
$2 x^{2} - 34 x + 132 = 0$
$x^{2} - 17 x + 66 = 0$
$x^{2} - 11 x - 6 x + 66 = 0$
$x (x - 11) - 6 (x - 11) = 0$
$(x - 11) (x - 6) = 0$
$x = 11, 6$