Question

sum of two numbers is 24 and their product is 143 find the sum of their squaue

Answer 1

let the two numbers are ( a, b ).

sum of two numbers = 24

a + b = 24

product = 143 => ab = 143

since , a + b = 24

on squaring both side , get

( a + b )^2 = ( 24 )^2

a^2 + b^2 + 2ab = 576

here, put Value of ab = 143 , we get

a^2 + b^2 + 2 ( 143 ) = 576

a^2 + b^2 + 286 = 576

a^2 + b^2 = 576 - 286

a^2 + b^2 = 290

Answer: sum of their squares = 290

-------------------------------------------------------

Answer 2

Let us assume the numbers are a and b.
Given :
a + b = 24
a*b = 143
As we know,
(a + b) ^2 = a^2 + b^2 +2*a*b
Now, By putting the values,
24^2 = a^2 + b^2 + 2*143
=> 576 = a^2 + b^2 + 286
=> a^2 + b^2 = 576-286 = 290.
Thus, the sum of their square will be 290.