Secondary 2 Maths

Given that (5x - 5y) ^ 2 = 500 and xy = 5 find the value of (x ^ 2 + y ^ 2).

Algebra
Jeffrey 1 Jeffrey 1
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1 Answer

We have
\[500=(5x-5y)^2=(5x)^2+(5y)^2 -2\cdot (5 x)(5y)=25x^2+25y^2-50xy.\]
Since $xy=5$,
\[500=25x^2+25y^2-50xy=25x^2+25y^2-50\cdot 5=25x^2+25y^2-250\]
\[\Rightarrow 500+250=25x^2+25y^2\]
\[\Rightarrow 750=25(x^2+y^2)\]
\[\Rightarrow x^2+y^2=\frac{750}{25}=30.\]

Savionf Savionf
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