Question

Solve this help me

It is the question of class 10 Maths​​

Answer 1

`x = \left ( \frac{ \left (3 ^{(2)/(3) } + 1 \right ) ^2}{3 ^{(2)/(3) } } \right )^{(1)/(2) } =\frac{ 3 ^{(2)/(3) } + 1 }{3 ^{(1)/(3) } }`

`(9 \cdot x + 10)/(3) = \left ( \frac{ 3 ^{(2)/(3) } + 1 }{3 ^{(1)/(3) } } \right )^3 } = x^3`

Therefore;

`x = \sqrt[3]{(9 \cdot x + 10)/(3)}`

Explanation:

Given that we have;

`x^2 - 2 = 3 ^{(2)/(3) } + 3 ^{-(2)/(3) }`

`x^2 = 3 ^{(2)/(3) } + 3 ^{-(2)/(3) } + 2 = \frac{3 ^{(4)/(3) } + 1 + 2 * 3 ^{(2)/(3) }}{3 ^{(2)/(3) } } = 3 ^{-(2)/(3) } * \left ( 3 ^{(4)/(3) } + 1 + 2 * 3 ^{(2)/(3) } \right )`

`x^2 = 3 ^{-(2)/(3) } * \left ( 3 ^{(4)/(3) } + 1 + 2 * 3 ^{(2)/(3) } \right )`

`x = 3 ^{-(1)/(3) } * \left ( 3 ^{(4)/(3) } + 1 + 2 * 3 ^{(2)/(3) } \right )^{(1)/(2) }`

`x = \sqrt{ \frac{3 ^{(4)/(3) } + 1 + 2 * 3 ^{(2)/(3) }}{3 ^{(2)/(3) } } } = \left ( \frac{3 ^{(4)/(3) } + 1 + 2 * 3 ^{(2)/(3) }}{3 ^{(2)/(3) } } \right )^{(1)/(2) }`

`x = \sqrt{ \frac{3 ^{(4)/(3) } + 1 + 2 * 3 ^{(2)/(3) }}{3 ^{(2)/(3) } } } = \left ( \frac{3 ^{(4)/(3) } + 1 + 2 * 3 ^{(2)/(3) }}{3 ^{(2)/(3) } } \right )^{(1)/(2) } = \left ( \frac{3 ^{(4)/(3) } + 2 * 3 ^{(2)/(3) } + 1}{3 ^{(2)/(3) } } \right )^{(1)/(2) }`

`x = \sqrt{ \frac{3 ^{(4)/(3) } + 1 + 2 * 3 ^{(2)/(3) }}{3 ^{(2)/(3) } } } = \left ( \frac{3 ^{(4)/(3) } + 2 * 3 ^{(2)/(3) } + 1}{3 ^{(2)/(3) } } \right )^{(1)/(2) } = \left ( \frac{ \left (3 ^{(2)/(3) } + 1 \right ) ^2}{3 ^{(2)/(3) } } \right )^{(1)/(2) }`

`x = \left ( \frac{ \left (3 ^{(2)/(3) } + 1 \right ) ^2}{3 ^{(2)/(3) } } \right )^{(1)/(2) } =\frac{ 3 ^{(2)/(3) } + 1 }{3 ^{(1)/(3) } }`

`(9 \cdot x + 10)/(3) = 3 \cdot x + (10)/(3) = 3 * \frac{ 3 ^{(2)/(3) } + 1 }{3 ^{(1)/(3) } } +(10)/(3) = \frac{ 3 ^{(5)/(3) } + 3 }{3 ^{(1)/(3) } } + (10)/(3)= \frac{ 3 ^{(7)/(3) } + 3 ^{(2)/(3) }*3+ 10 }{3 } } }`

`(9 \cdot x + 10)/(3) =\frac{ 3 ^{(7)/(3) } + 3 ^{(2)/(3) }*3+ 10 }{3 } } } = \frac{ 3 ^{(7)/(3) } + 3 ^{(5)/(3) }+ 10 }{3 } } } = \left ( \frac{ 3 ^{(2)/(3) } + 1 }{3 ^{(1)/(3) } } \right )^3 } = x^3`

Therefore;

`x^3 = (9 \cdot x + 10)/(3)`

`x = \sqrt[3]{(9 \cdot x + 10)/(3)}`