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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Expert Answer

Clara Reese
Answered 2021-01-24 Author has 120 answers

Calculation:
Let two negative numbers are x and y.
The sum of the square of two negative numbers is 106.
x2+y2=106 (1)
And the difference of the square of the number is 56.
x2y2=56 (2)
Add equation (1) and (2).
(x2+y2)+(x2y2)=106+56
2x2+0=162
2x2=162
(2x2)/2=162/2 [Divide by 2]
x2=81
Taking square root.
x2=±81
x=±92
x=±9
x=-9, because x is negative
Substitute x = -9 in equation (1).
92+y2=106
81+y2=106
81+81+y2=10681 [Substract 81 from both sides]
=y2=25
Taking square root.
y2=±25
y=52
y=±5
y=-5, because y is negative
Thus, the negative numbers are x = -9 and y = -5.

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