Question

Three numbers x, y, z are such that
x2 + y2 = z2; If z = m² + n^2, y = 2mn, then
1/x + 1/z is equal to

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Answer 1

Step-by-step explanation:

x^2+y^2=z^2

m^2+n^2=z

y=2mn

x^2+y^2=m^4+n^4

x^2+2m^2n^2=m^4+n^4

x^2=m^4+n^4 -2m^2n^2

x^2=(m^2-n^2)^2

x=m^2-n^2

1/x +1/z

=1/m^2-n^2 +1/m^2+n^2

=2m^2/m^4-n^4