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Semmy [17]
3 years ago
15

If (x-y)^2=100 and xy=20. what's the value of x^2+y^2?

Mathematics
2 answers:
ahrayia [7]3 years ago
8 0

(x-y)^2=x^2-2xy+y^2=(x^2+y^2)-2(xy)\\\\\text{We have}\ (x-y)^2=100\ \text{and}\ xy=20.\\\\\text{Substitute}\\\\100=(x^2+y^2)-2(20)\\100=(x^2+y^2)-40\qquad\text{add 40 to both sides}\\\\140=(x^2+y^2)\\\\Answer:\ \boxed{x^2+y^2=140}

Flauer [41]3 years ago
7 0

<u>Answer:</u> The value of x^2+y^2 is 140

<u>Step-by-step explanation:</u>

We are given an expression:

(x-y)^2=100

And,

xy = 20

Using the identity:

(a-b)^2=a^2+b^2-2ab

Solving the expression:

x^2+y^2-2xy=100

Putting the value of 'xy' in above equation, we get:

x^2+y^2-2(20)=100\\\\x^2+y^2=100+40\\\\x^2+y^2=140

Hence, the value of x^2+y^2 is 140

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