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Algebraic Identities

Question

Evaluate
$(2 - \frac{7}{2})^{2} + (3 + \frac{5}{2})^{2} = r^{2}$ .

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Solution

Verified by Toppr

${(2 - \frac{7}{2})}^{2} + {(3 + \frac{5}{2})}^{2} = r^{2}$
${(\frac{4 - 7}{2})}^{2} + {(\frac{6 + 5}{2})}^{2} = r^{2}$
${(\frac{- 3}{2})}^{2} + {(\frac{11}{2})}^{2} = r^{2}$
$(\frac{9}{4}) + (\frac{121}{4}) = r^{2}$
$\frac{9 + 121}{4} = r^{2}$
$\frac{130}{4} = r^{2}$
$\frac{65}{2} = r^{2}$
$r = \sqrt{\frac{65}{2}}$

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