Question

if a^2+b^2+1/a^2+1/b^2=4, then find the value of root a^2 +b^2​

Answer 1

a²+b²+(1/a)²+(1/b)² = 4

=> a²-2(a)(1/a)+(1/a²)+b²-2(b)(1/b)+(1/b²) = 4-2-2

=> {a-(1/a)}²+{b-(1/b)}² = 0

∵ a,b are real numbers

∴ a-(1/a) = 0 => a = 1/a => a² = 1

b-(1/b) = 0 => b = 1/b => b² = 1

∴√(a²+b²) = √(1+1) = √2 <===== ANSWER

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