Two integers differ by 12 and the sum of their squares is 74. Find the integers.

The answers are : -7 and 5 or 7 and -5.

Could you please show me how to work this problem out?

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- Feb 12th 2010, 01:10 PMTessarinaProblem solving with Quadratics
Two integers differ by 12 and the sum of their squares is 74. Find the integers.

The answers are : -7 and 5 or 7 and -5.

Could you please show me how to work this problem out? - Feb 12th 2010, 01:22 PMJhevon
- Feb 12th 2010, 02:26 PMTessarina
- Feb 12th 2010, 02:33 PMicemanfan
Substitute

$\displaystyle x = y + 12$

into the equation $\displaystyle x^2 + y^2 = 74$

yielding $\displaystyle (y + 12)^2 + y^2 = 74$,

which can be solved using the quadratic formula. - Feb 12th 2010, 07:08 PMTessarina
- Feb 13th 2010, 04:19 AMGrandad
Hello Tessarina$\displaystyle (y+12)^2+y^2=74$

$\displaystyle \Rightarrow y^2+24y+144+y^2=74$

$\displaystyle \Rightarrow 2y^2+24y +70=0$

$\displaystyle \Rightarrow y^2+12y+35=0$

$\displaystyle \Rightarrow (y+5)(y+7)=0$

$\displaystyle \Rightarrow y = -5, -7$

$\displaystyle \Rightarrow x = y+12 = 7, 5$

So the solutions are $\displaystyle (7, -5)$ and $\displaystyle (5, -7)$.

Grandad