Question

Solve it.
$\Huge{\sqrt{\dfrac{81}{64}\sqrt{\dfrac{81}{64}\sqrt{\dfrac{81}{64}\sqrt{\dfrac{81}{64}}}}......\infty }}}} = \Huge{\text{?}}$

Answer 1

Answer:

(81/64)

Step-by-step explanation:

$Given:\sqrt{\frac{81}{64}\sqrt{\frac{81}{64}}\sqrt{\frac{81}{64}}\sqrt{\frac{81}{64}} ..\infty}}$

$Let, x =\sqrt{\frac{81}{64}\sqrt{\frac{81}{64}}\sqrt{\frac{81}{64}}+... \infty}}$

On squaring both sides, we get

$x^2=\frac{81}{64}*\sqrt{\frac{81}{64}*\sqrt{\frac{81}{64}}*\sqrt{\frac{81}{64}}.... \infty}}$

$=>x^2 =\frac{81}{64} * x$

$=>x^2=\frac{81x}{64}$

$=>x^2-(\frac{81x}{64})=0$

$=>x(x - \frac{81}{64}) = 0$

$x=0, \frac{81}{64}$

It is impossible that x = 0 because (√81/64) > 0, So We reject x = 0.

Therefore, the value of x = (81/64).

Hope it helps!

Answer 2

ANSWER:-----

Answer:

(81/64)answer because

explanation:

On squaring both sides, we get

=>x2=8164∗x=>x^2 =\frac{81}{64} * x=>x2=6481∗x

=>x2=81x64=>x^2=\frac{81x}{64}=>x2=6481x

=>x2−(81x64)=0=>x^2-(\frac{81x}{64})=0=>x2−(6481x)=0

=>x(x−8164)=0=>x(x - \frac{81}{64}) = 0=>x(x−6481)=0

x=0,8164x=0, \frac{81}{64}x=0,6481

It is impossible that x = 0 because (√81/64) > 0, So We reject x = 0.

hence. the value of x = (81/64).

Hope it helps!