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Easy to guess, somewhat hard to prove!

Algebra Level 2

If $x^{2}$ + $a^{2}$ = $y^{2}$ + $b^{2}$ = ( $a\times x$ ) + ( $b\times y$ ) = 1,

then the numerical value of $a^{2}$ + $b^{2}$ is

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by jaiveer shekhawat

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