If x(2x + 3) = 90 and 7y -1/2 + 2y -1/2 = y 1/2 (x and y are positive numbers), then what is the value of x 2+ y 2?
117
Step 1 — Find x: \(2x^2+3x-90=0\) factors as \((x-6)(2x+15)=0\). Since \(x>0\), \(x=6\).
Step 2 — Find y: Treating the equation as \(9y^{-1/2}=y^{1/2}\) gives \(y=9\).
Therefore \(x^2+y^2=36+81=\mathbf{117}\).
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