The number of integral solutions of the equation 1-7-4 -3x2-3 x-1-1-7-4 -322-3 x-1-14 is

The correct option is D 41/(7 4√(3))^x^2 3x+1+1/(7+4√(3))^x^2 3x+1= 14 ⇒ t+1/t=14 ( t=(7+4√(3))^x^2 3x+1 ) ⇒ t^2 14t+1=0 ⇒ t=7± 4√(3) (7+4√(3))^x^2 3x+1=(7+ ...

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Byju's Answer

Standard XII

Mathematics

Higher Order Equations

The number of...

Question

The number of integral solutions of the equation $\frac{1}{(7 - 4 \sqrt{3})^{x^{2} - 3 x + 1}} + \frac{1}{(7 + 4 \sqrt{3})^{x^{2} - 3 x + 1}} = 14$ is

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Solution

The correct option is D 4
$\frac{1}{(7 - 4 \sqrt{3})^{x^{2} - 3 x + 1}} + \frac{1}{(7 + 4 \sqrt{3})^{x^{2} - 3 x + 1}} = 14 \Rightarrow t + \frac{1}{t} = 14 (t = (7 + 4 \sqrt{3})^{x^{2} - 3 x + 1}) \Rightarrow t^{2} - 14 t + 1 = 0 \Rightarrow t = 7 \pm 4 \sqrt{3} (7 + 4 \sqrt{3})^{x^{2} - 3 x + 1} = (7 + 4 \sqrt{3}) a n d (7 + 4 \sqrt{3})^{x^{2} - 3 x + 1} = \frac{1}{(7 + 4 \sqrt{3})} ∴ x^{2} - 3 x + 1 = \pm 1 \Rightarrow x = 0, 3, 1, 2$

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Similar questions

Q. Integrate wrt x

\frac{1}{\sqrt{(3 x + 4)} - \sqrt{(3 x + 1)}} + \frac{8 x + 13}{\sqrt{(4 x + 7)}} + (7 x - 2) \sqrt{3 x + 2} .

Solve each of the following equations and also verify your solution :

$\frac{(3 x + 1)}{16} + \frac{(2 x - 3)}{7} = \frac{(x + 3)}{8} + \frac{(3 x - 1)}{14}$

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Q. What is the value of

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The number of integral solutions of the equation 1(7−4√3)x2−3x+1+1(7+4√3)x2−3x+1=14 is

The correct option is D 41(7−4√3)x2−3x+1+1(7+4√3)x2−3x+1=14⇒t+1t=14(t=(7+4√3)x2−3x+1)⇒t2−14t+1=0⇒t=7±4√3(7+4√3)x2−3x+1=(7+4√3)and(7+4√3)x2−3x+1=1(7+4√3)∴ x2−3x+1=±1⇒x=0,3,1,2

The number of integral solutions of the equation $\frac{1}{(7 - 4 \sqrt{3})^{x^{2} - 3 x + 1}} + \frac{1}{(7 + 4 \sqrt{3})^{x^{2} - 3 x + 1}} = 14$ is