Question

x = 2^1/3 + 2^2/3 , show that x^3 - 6x = 2

Answer 1

Given that :-
9^(x+2)=240+9^x
9^x*9^2=240+9^x
9^x*81-9^x=240
9^x(81-1)=240
9^x=240/80
9^x=3
3^2x=1
2x=1
x=1/2
Now,
(8*x)^x
(8*1/2)^1/2
(4)^1/2
(2^2)^1/2
(2)^2*1/2
=2

Answer 2

Answer:

GIVEN that:-

9^(x + 2) = 240 + 9^x

⇒9^x × 9² = 240 + 9^x

⇒9^x × 81 - 9^x = 240

⇒9^x(81 - 1) = 240

⇒9^x = 240/80

⇒9^x = 3

⇒3^2x = 3¹

⇒2x = 1

⇒x = 1/2

Now,

(8 × x)^x

⇒(8 × 1/2)½

⇒ (4)½

⇒(2²)½

⇒ (2)^2 × 1/2

⇒ 2

Step-by-step explanation:

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