 # The sum of the squares of two negative numbers is 106 and the difference of the squares of the number is 56 find the numbers abondantQ 2021-01-23 Answered
The sum of the squares of two negative numbers is 106 and the difference of the squares of the number is 56 find the numbers
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Calculation:
Let two negative numbers are x and y.
The sum of the square of two negative numbers is 106.
${x}^{2}+{y}^{2}=106$ (1)
And the difference of the square of the number is 56.
${x}^{2}-{y}^{2}=56$ (2)
$\left({x}^{2}+{y}^{2}\right)+\left({x}^{2}-{y}^{2}\right)=106+56$
$2{x}^{2}+0=162$
$2{x}^{2}=162$
$\left(2{x}^{2}\right)/2=162/2$ [Divide by 2]
${x}^{2}=81$
Taking square root.
$\sqrt{{x}^{2}}=±\sqrt{81}$
$x=±\sqrt{{9}^{2}}$
$x=±9$
x=-9, because x is negative
Substitute x = -9 in equation (1).
$-{9}^{2}+{y}^{2}=106$
$81+{y}^{2}=106$
$-81+81+{y}^{2}=106-81$ [Substract 81 from both sides]
$={y}^{2}=25$
Taking square root.
$\sqrt{{y}^{2}}=±\sqrt{25}$
$y=\sqrt{{5}^{2}}$
$y=±5$
y=-5, because y is negative
Thus, the negative numbers are x = -9 and y = -5.