Question : If $x-y=7$ and $xy=32$, then the value of $x^{2}+y^{2}$ is:
Option 1: 49
Option 2: 64
Option 3: 113
Option 4: 15
Answer (1)
26th Jan, 2024
Correct Answer: 113
Solution :
Given: $x-y=7$ and $xy=32$.
We know that $(x-y)^{2}=x^{2}+y^{2}-2xy$.
⇒ $x^{2}+y^{2}=(x-y)^{2}+2xy$
By putting the value of $x-y=7$ and $xy=32$ in above expression, we get:
⇒ $x^{2}+y^{2}=7^{2}+2×32$
⇒ $x^{2}+y^{2}=49+64$
⇒ $x^{2}+y^{2}=113$
Hence, the correct answer is 113.
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