Question

addition of two numbers is 23 while multiplication is 120. Find the addition of square of both the numbers.​

Answer 1

Answer:

289

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Answer 2

Answer:

Two numbers are 15 and 8

sum of squares = 289

Step-by-step explanation:

Let the two numbers be ' x ' and ' y '

Addition of two numbers = 23

=> x + y = 23 ............. eq1

Multiplication of two numbers = 120

=> x*y = 120

=> xy = 120 .............eq 2

From eq 1

x + y = 23

=> y = 23 - x

Substitute y = 23 - x in eq 2

xy = 120

=> x ( 23 - x ) = 120

=> 23x - x^2 = 120

=> 0 = 120 - 23x + x ^2

=> x^2 - 23x + 120 = 0

No solve quadratic equation

x^2 - 23x + 120 = 0

=> x^2 - 15x - 8x + 120 = 0

=> x ( x - 15 ) - 8 ( x - 15 )=0

=> ( x - 15 ) ( x - 8 ) = 0

=> x - 15 = 0 OR x - 8 = 0

=> x = 15 OR x = 8

Now substitute x = 15 OR x = 8 in eq 1

x + y = 23

=> 15 + y = 23 OR 8 + y = 23

=> y = 23 - 15 OR y = 23 - 8

=> y = 8 OR y = 15

Hence, when x = 15 value of y will be 8

And when x = 8 value of y will be 15

Addition of squares of both the number

15^2 + 8^2

=> 225 + 64

=> 289