Question

A sum of two numbers is 24 and their product is 143 the sum of their squares is solution short answer

Answer 1

This is your answer

Answer 2

Answer:

The sum of the squares of the given numbers will be 290.

Solution:

Given,

Let the two numbers be x and y.

Their sum will be,

x + y = 24

Their product will be,

$\begin{aligned} x y & = 143 \\\\ y & = \frac { 143 } { x } \end{aligned}$

Substitute the value of y in the first equation,

$\begin{array} { c } { x + \frac { 143 } { x } = 24 } \\\\ { \frac { x ^ { 2 } + 143 } { x } = 24 } \\\\ { x ^ { 2 } + 143 = 24 x } \\\\ { x ^ { 2 } - 24 x + 143 = 0 } \end{array}$

$\begin{array} { c } { x ^ { 2 } - 11 x - 13 x + 143 = 0 } \\\\ { x ( x - 11 ) - 13 ( x - 11 ) = 0 } \\\\ { \quad ( x - 11 ) ( x - 13 ) = 0 } \\\\ { x = 11 \text { or } 13 } \end{array}$

Thus, the value of y will be

$y = \frac { 143 } { x }$

If x = 11,

$y = \frac { 143 } { 11 } = 13$

If x = 13,

$y = \frac { 143 } { 13 } = 11$

Thus, the value of their squares will be,

If x = 11 and y = 13,

$\begin{array} { l } { x ^ { 2 } + y ^ { 2 } = 11 ^ { 2 } + 13 ^ { 2 } } \\\\ { = 121 + 169 = 290 } \end{array}$

If x = 13 and y = 11,

$\begin{array} { l } { x ^ { 2 } + y ^ { 2 } = 13 ^ { 2 } + 11 ^ { 2 } } \\\\ { = 169 + 121 = 290 } \end{array}$

Thus, the value of their squares will be 290.