Question

The difference of two positive whole numbers is 3 and the sum of their squares is 117.find the 2 numbers

Answer 1

Difference is 9 and 6

Answer 2

Answer:

Required two numbers are

Required two numbers are 9,6

Step-by-step explanation:

Let x,(x-3) are two positive whole numbers.

According to the problem given,

x²+(x-3)²=117

$\implies x^{2}+x^{2}-2\times x\times 3+3^{2}=117$

$\implies 2x^{2}-6x+9-117=0$

$\implies 2x^{2}-6x-108=0$

/* Divide each term by 2, we get

$\implies x^{2}-3x-54=0$

/* Splitting the middle term, we get

$\implies x^{2}-9x+6x-54=0$

$\implies x(x-9)+6(x-9)=0$

$\implies (x-9)(x+6)=0$

$\implies x-9=0 \: Or \:x+6=0$

$\implies x=9 \: Or \:x=-6$

But , x is a whole number.

x = 9

Required two numbers are x,x-3

9,6

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