Question

Hello User!

Give me the solution of the Question in the attachment.

Answer only by Wizard rank holders, mods, brainly stars and serious (topper) users.


Radhey Radhey​

Answer 1

Answer:

5

Explanation:

For our convinience let us assume ( 20x + 13 ) = a³

³√[ 20x + ³√( 20x + 13 ) ] = 13

On cubing on both sides

=> 20x + ³√( a³ ) = 13³

=> 20x + a = 13³

On adding 13 on both sides

=> 20x + 13 + a = 13³ + 13

=> a³ + a = 13³ + 13

Comparing on both sides

• a³ = 13³

=> 20x + 13 = 13³

=> 20x + 13 = 13³

=> 20x = 13³ - 13

=> 20x = 13 ( 13² - 1 )

=> 20x = 13 ( 168 )

=> 5x = 13 ( 42 )

=> x = 13 × 42 / 5

=> x = 546 / 5

Hence x is expressed in a/b where they relatively prime and a real value.

=> b = 5

Therefore the value of b is 5.

Answer 2

Given,

$\longrightarrow \sqrt[3]{20x+\sqrt[3]{20x+13}}=13$

Cubing both sides,

$\longrightarrow 20x+\sqrt[3]{20x+13}=13^3$

Adding 13 to both sides,

$\longrightarrow 20x+\sqrt[3]{20x+13}+13=13^3+13$

$\longrightarrow (20x+13)+\sqrt[3]{20x+13}=13^3+13$

$\longrightarrow \left(\sqrt[3]{20x+13}\right)^3+\sqrt[3]{20x+13}=13^3+13$

Now, without loss of generality,

$\longrightarrow\sqrt[3]{20x+13}=13$

$\longrightarrow20x+13=13^3$

$\longrightarrow20x=13^3-13$

$\longrightarrow20x=2184$

$\longrightarrow x=\dfrac{2184}{20}$

$\longrightarrow x=\dfrac{546}{5}$

Now $x$ is in simplest form, where 5 and 546 are relatively prime. Hence,

$\longrightarrow a=546$

$\longrightarrow\underline{\underline{b=5}}$

Hence 5 is the answer.