Question

The sum of two numbers is 24 and their produvt is 143. What is sum of their squares

Answer 1

$\bold{Answer:}$

$\bold{290}$

$\bold{Step} - \bold{by} - \bold{step\ explanation:}$

$Let the numbers be \ x\ and \ y. \\ \\ x + y = 24 \\ \\ xy = 143$

$(x + y)^2 = 24^2 \\ \\ x^2 + y^2 + 2xy = 576 \\ \\ x^2 + y^2 + 2 \times 143 = 576 \\ \\ x^2 + y^2 + 286 = 576 \\ \\ x^2 + y^2 = 576 - 286 = \bold{290}$

$Hope this may be helpful. \\ \\ Thank you. Have a nice day. \\ \\ \\ \#adithyasajeevan$

Answer 2

Let X and Y be the two numbers

Given:

=> X + Y = 24

=> X = 24 - Y. ------ 1

=> XY = 143. ---------2

Sub 1 and 2

XY = 143

(24 - Y) Y = 143

24Y - Y^2 = 143

Y^2 - 24Y + 143 = 0

Factorize

Y^2 - 13Y - 11Y + 143 = 0

Y ( Y - 13 ) - 11 ( Y - 13 ) = 0

( Y - 13 ) ( Y - 11) = 0

Y = 13 or 11

If Y = 13

X = 24 - 13

X = 11

And the sum of their squares is

= X^2 + Y^2

= 11^2 + 13^2

= 121 + 169

= 290

If Y = 11

X = 24 - 11

X = 13

And the sum of their squares is

= X^2 + Y^2

= 13^2 + 11^2

= 169 + 121

= 290

Therefore the answer is 290