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If X − Y = 7 and Xy = 9, Find the Value of X2 + Y2 - Mathematics

Answer in Brief

If x − y = 7 and xy = 9, find the value of x2 + y2

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Solution

We have:

\[\left( x - y \right)^2 = x^2 - 2xy + y^2 \]

\[ \Rightarrow x^2 + y^2 = \left( x - y \right)^2 + 2xy\]

\[\Rightarrow x^2 + y^2 = 7^2 + 2 \times 9\]      (\[\because\]  \[x - y = 7 \text { and } xy = 9\])

\[\Rightarrow x^2 + y^2 = 7^2 + 2 \times 9\]

\[ \Rightarrow x^2 + y^2 = 49 + 18\]

\[ \Rightarrow x^2 + y^2 = 67\]

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APPEARS IN

RD Sharma Class 8 Maths
Chapter 6 Algebraic Expressions and Identities
Exercise 6.6 | Q 11 | Page 43
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