Name: Proportion
Uploaded: 2019-07-19
Duration: 5 min 17 s
Description: A T-Rex looks strange because it has disproportionately sized arms. But, what are proportions? To understand their significance in mathematics, here are some...

Question

Using properties of proportion, find $x$ from the following equations:

$\frac{\sqrt{1 + x} + \sqrt{1 - x}}{\sqrt{1 + x} - \sqrt{1 - x}} = \frac{a}{b}$

Accepted Answer

Given: $\frac{\sqrt{1 + x} + \sqrt{1 - x}}{\sqrt{1 + x} - \sqrt{1 - x}} = \frac{a}{b}$

By applying componendo and dividendo rule for the given

$\Rightarrow \frac{\sqrt{1 + x} + \sqrt{1 - x} + \sqrt{1 + x} - \sqrt{1 - x}}{\sqrt{1 + x} + \sqrt{1 - x} - \sqrt{1 + x} + \sqrt{1 - x}} = \frac{a + b}{a - b}$

$\Rightarrow \frac{2 \sqrt{1 + x}}{2 \sqrt{1 - x}} = \frac{a + b}{a - b}$

$\Rightarrow \frac{\sqrt{1 + x}}{\sqrt{1 - x}} = \frac{a + b}{a - b}$

Squaring on both sides

$\Rightarrow \frac{1 + x}{1 - x} = \frac{(a + b)^{2}}{(a - b)^{2}}$

Again by applying componendo and dividendo rule for the given

$\Rightarrow \frac{1 + x + 1 - x}{1 + x - 1 + x} = \frac{(a + b)^{2} + (a - b)^{2}}{(a + b)^{2} - (a - b)^{2}}$

$\Rightarrow \frac{2}{2 x} = \frac{2 (a^{2} + b^{2})}{4 ab}$

$\Rightarrow \frac{1}{x} = \frac{a^{2} + b^{2}}{2 ab}$

On cross multiplication we get

$\Rightarrow x = \frac{2 ab}{a^{2} + b^{2}}$

Hence, the value of $x$ is $\frac{2 ab}{a^{2} + b^{2}}$ .

Using properties of proportion, find $x$ from the following equations:

$\frac{\sqrt{1 + x} + \sqrt{1 - x}}{\sqrt{1 + x} - \sqrt{1 - x}} = \frac{a}{b}$

Important Questions on Ratio and Proportion

Learn and Prepare for any exam you want !

Using properties of proportion, find x from the following equations: 1+x+1-x1+x-1-x=ab

Important Questions on Ratio and Proportion

Learn and Prepare for any exam you want !

Using properties of proportion, find $x$ from the following equations:

$\frac{\sqrt{1 + x} + \sqrt{1 - x}}{\sqrt{1 + x} - \sqrt{1 - x}} = \frac{a}{b}$