Solve for x- - 36x-1 -6- x - 36x-1 -6- x -9

√(36x+1)+6√(x)√(36x+1) 6√(x)=√(36x+1)+6√(x)√(36x+1) 6√(x)×√(36x+1)+6√(x)√(36x+1)+6√(x)=(√(36x+1)+6√(x))^2(√(36x+1))^2 (6√(x))^2=72x+1+12√(36x^2+x)=9 7 ...

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Byju's Answer

Standard IX

Mathematics

Zeroes of a Polynomial

Solve for x...

Question

Solve for $x$ : $\frac{\sqrt{36 x + 1} + 6 \sqrt{x}}{\sqrt{36 x + 1} - 6 \sqrt{x}} = 9$

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Solution

$\frac{\sqrt{36 x + 1} + 6 \sqrt{x}}{\sqrt{36 x + 1} - 6 \sqrt{x}} = \frac{\sqrt{36 x + 1} + 6 \sqrt{x}}{\sqrt{36 x + 1} - 6 \sqrt{x}} \times \frac{\sqrt{36 x + 1} + 6 \sqrt{x}}{\sqrt{36 x + 1} + 6 \sqrt{x}} = \frac{(\sqrt{36 x + 1} + 6 \sqrt{x})^{2}}{(\sqrt{36 x + 1})^{2} - (6 \sqrt{x})^{2}} = 72 x + 1 + 12 \sqrt{36 x^{2} + x} = 9$
$72 x + 12 \sqrt{36 x^{2} + x} = 8 ⟹ (2 - 18 x)^{2} = 9 (36 x^{2} + x)$
$x = \frac{4}{81}$

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Solve for x: √36x+1+6√x√36x+1−6√x=9

√36x+1+6√x√36x+1−6√x=√36x+1+6√x√36x+1−6√x×√36x+1+6√x√36x+1+6√x=(√36x+1+6√x)2(√36x+1)2−(6√x)2=72x+1+12√36x2+x=972x+12√36x2+x=8⟹(2−18x)2=9(36x2+x)x=481

Solve for $x$ : $\frac{\sqrt{36 x + 1} + 6 \sqrt{x}}{\sqrt{36 x + 1} - 6 \sqrt{x}} = 9$