+1661 Define f(x)=1x+1x and g(x)=1x−1x. Find the square of the largest real solution to the equation (g(x))2−(f(x))2=1.
+15070 Find the square of the largest real solution to the equation (g(x))2−(f(x))2=1.
Hello wiseowl!
(g(x))2−(f(x))2=11(x−1x)2−1(x+1x)2=1
1(x2−1x)2−1(x2+1x)2=1
x2(x2−1)2−x2(x2+1)2=1
4x4(x−1)2(x+1)2(x2+1)2=1
Calculated by WolframAlpha.
x=−√√2−1x=√√2−1x=−√1+√2x=√1+√2
x∈{−1.55377,−0.64359,0.64359,1.55377}
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