Question

If $x^2$ + $y^2$ = $z^2$. Then which of the following is/are true?

• A. 2 = 1 +
• B. 2 = 1 +
• C. 2 = 1 +
• D. 2 = 1 +

Answer 1

Answer: (A), (B)

The correct options are
A

2 = 1 +

B

2 = 1 +

Given $x^2$ + $y^2$ = $z^2$

$x^2$ = $z^2$ - $y^2$

$x^2$ = (z-y) (z+y)

Taking logarithms on both sides on base (z+y) and (z-y) respectively.

We get,

2${\log }_{y+z}{x}^2$ = ${\log }_{y+z}(y+z)$ + ${\log }_{y+z}(z-y)$

2${\log }_{y+z}x$ = 1 + ${\log }_{y+z}(z-y)$

${\log }_{z-y}{x}^2$ = ${\log }_{z-y}(z-y)$ + ${\log }_{z-y}(y+z)$ (Taking log with base (z-y))

2${\log }_{z-y}x$ = 1 + ${\log }_{z-y}(y+z)$