X^2a=Y^2b=Z^2c and X^2=YZ find (AB+BC+CA)/AB where (X,Y,Z not equal to zero
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(ab+bc+ca)/ab = (x² + y² + z² )/z²
Step-by-step explanation:
x²a = y²b = z²c
x² = yz
(ab+bc+ca)/ab
= 1 + c/a + c/b
x²a = z²c
=> c/a = x²/z²
=> c/a = yz/z²
=> c/a = y/z
y²b = z²c
=> c/b = y²/z²
=> c/b = y²/z²
1 + c/a + c/b
= 1 + y/z + y²/z²
= (z² + yz + y²)/z²
yz = x²
= (z² + x² + y²)/z²
= (x² + y² + z² )/z²
(ab+bc+ca)/ab = (x² + y² + z² )/z²
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