Using the properties of proportion- solve for x- -a-x-a-x-a-x-a-x-bA- 2 a b-b2-1B- a b-b2-1C- b 2-1-2 abD- a b-2 b2-1

The correct option is A By using the componendo and dividendo, we get 2√(a+x)/2√(a+x)=b+1/b+1 Now squaring both sides, we get a+x/a x=b^2+1+2b/b^2+1 2b Again u ...

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Standard X

Mathematics

Componendo and Dividendo

Using the pro...

Question

Using the properties of proportion, solve for x: $\frac{\sqrt{a + x} + \sqrt{a - x}}{\sqrt{a + x} - \sqrt{a - x}} = b$

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Solution

The correct option is A

By using the componendo and dividendo, we get $\frac{2 \sqrt{a + x}}{2 \sqrt{a + x}} = \frac{b + 1}{b + 1}$
Now squaring both sides, we get $\frac{a + x}{a - x} = \frac{b^{2} + 1 + 2 b}{b^{2} + 1 - 2 b}$
Again use componendo and dividend, to get the value of x.
$X = \frac{2 a b}{b^{2} + 1}$

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Using the properties of proportion, solve for x: √a+x+√a−x√a+x−√a−x=b

The correct option is A By using the componendo and dividendo, we get 2√a+x2√a+x=b+1b+1 Now squaring both sides, we get a+xa−x=b2+1+2bb2+1−2b Again use componendo and dividend, to get the value of x. ​X=2abb2+1

Using the properties of proportion, solve for x: $\frac{\sqrt{a + x} + \sqrt{a - x}}{\sqrt{a + x} - \sqrt{a - x}} = b$