If x- 4-6-2-3- Find the value of x-2-2-x-2-2-x-2-3-x-2-3- using the properties of proportion- 1-0-3-2-

The correct option is D 2 Given, x = 4√(6)/√(2)+√(3) It may be written as, x=2√(2)× 2√(3)/√(2)+√(3) or x/2√(2)=2√(3)/√(2)+√(3)…(i) By componendo and dividendo, ...

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Byju's Answer

Standard X

Mathematics

Componendo and Dividendo

If x= 4√(6)/√...

Question

If $x = \frac{4 \sqrt{6}}{\sqrt{2} + \sqrt{3}}$ . Find the value of $\frac{x + 2 \sqrt{2}}{x - 2 \sqrt{2}} + \frac{x + 2 \sqrt{3}}{x - 2 \sqrt{3}}$ , using the properties of proportion.

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Solution

The correct option is B
2

Given, $x = \frac{4 \sqrt{6}}{\sqrt{2} + \sqrt{3}}$
It may be written as,
$x = \frac{2 \sqrt{2} \times 2 \sqrt{3}}{\sqrt{2} + \sqrt{3}}$
or $\frac{x}{2 \sqrt{2}} = \frac{2 \sqrt{3}}{\sqrt{2} + \sqrt{3}} \dots (i)$
By componendo and dividendo, we get
$\frac{x + 2 \sqrt{2}}{x - 2 \sqrt{2}} = \frac{2 \sqrt{3} + \sqrt{2} + \sqrt{3}}{2 \sqrt{3} - \sqrt{2} - \sqrt{3}} = \frac{3 \sqrt{3} + \sqrt{2}}{\sqrt{3} - \sqrt{2}} \dots (i i)$
Equation (i) may also be written as
$\frac{x}{2 \sqrt{3}} = \frac{2 \sqrt{2}}{\sqrt{2} + \sqrt{3}}$
By componendo and dividendo, we get
$\frac{x + 2 \sqrt{3}}{x - 2 \sqrt{3}} = \frac{2 \sqrt{2} + \sqrt{2} + \sqrt{3}}{2 \sqrt{2} - \sqrt{2} - \sqrt{3}} = \frac{3 \sqrt{2} + \sqrt{3}}{\sqrt{2} - \sqrt{3}} \dots (i i i)$
Adding equation (ii) and (iii), we get
$\frac{x + 2 \sqrt{2}}{x - 2 \sqrt{2}} + \frac{x + 2 \sqrt{3}}{x - 2 \sqrt{3}} = \frac{3 \sqrt{3} + \sqrt{2}}{\sqrt{3} - \sqrt{2}} + \frac{3 \sqrt{2} + \sqrt{3}}{\sqrt{2} - \sqrt{3}} = \frac{3 \sqrt{3} + \sqrt{2}}{\sqrt{3} - \sqrt{2}} - (\frac{3 \sqrt{2} + \sqrt{3}}{\sqrt{3} - \sqrt{2}}) = \frac{3 \sqrt{3} + \sqrt{2} - 3 \sqrt{2} - \sqrt{3}}{\sqrt{3} - \sqrt{2}} = \frac{2 \sqrt{3} - 2 \sqrt{2}}{\sqrt{3} - \sqrt{2}} = \frac{2 (\sqrt{3} - \sqrt{2})}{\sqrt{3} - \sqrt{2}} = 2$

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Q. If

x = \frac{4 \sqrt{6}}{\sqrt{2} + \sqrt{3}}

. find the value of

\frac{x + 2 \sqrt{2}}{x - 2 \sqrt{2}} + \frac{x + 2 \sqrt{3}}{x - 2 \sqrt{3}}

, using the properties of proportion.

If $x = \frac{4 \sqrt{6}}{\sqrt{2} + \sqrt{3}}$ . Find the value of $\frac{x + 2 \sqrt{2}}{x - 2 \sqrt{2}} + \frac{x + 2 \sqrt{3}}{x - 2 \sqrt{3}}$ , using the properties of proportion.

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If x=4√6√2+√3. Find the value of x+2√2x−2√2+x+2√3x−2√3, using the properties of proportion.

If $x = \frac{4 \sqrt{6}}{\sqrt{2} + \sqrt{3}}$ . Find the value of $\frac{x + 2 \sqrt{2}}{x - 2 \sqrt{2}} + \frac{x + 2 \sqrt{3}}{x - 2 \sqrt{3}}$ , using the properties of proportion.