What is the answer to (sqrt(5+\sqrt{24)})^x+(sqrt(5-\sqrt{24)})^x=10 ?

The answer to (sqrt(5+\sqrt{24)})^x+(sqrt(5-\sqrt{24)})^x=10 is x=2,x=-2

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(sqrt(5+\sqrt{24)})^x+(sqrt(5-\sqrt{24)})^x=10

(5 + 24)^{x} + (5 - 24)^{x} = 10

x = 2, x = - 2

Solution steps

(5 + 24)^{x} + (5 - 24)^{x} = 10

Apply exponent rules

(5 + 24)^{x} + ((5 + 24)^{x})^{- 0.5} = 10

Rewrite the equation with

(5 + 24)^{x} = u

u + (u)^{- 0.5} = 10

Solve

u + u^{- 0.5} = 10 : u = 49 + 206, u = 49 - 206

u = 49 + 206, u = 49 - 206

Substitute back

u = (5 + 24)^{x},

solve for

x

Solve

(5 + 24)^{x} = 49 + 206 : x = 2

Solve

(5 + 24)^{x} = 49 - 206 : x = - 2

x = 2, x = - 2

7^{1 - x} = 4 9^{3 x + 1}

x, e^{y} = 2^{x}

2^{2 x} - 2^{x + 1} = 8

9^{x} = 3^{x} - 3

x, b = a \cdot (1 + \frac{63}{100})^{x}

What is the answer to (sqrt(5+\sqrt{24)})^x+(sqrt(5-\sqrt{24)})^x=10 ?
The answer to (sqrt(5+\sqrt{24)})^x+(sqrt(5-\sqrt{24)})^x=10 is x=2,x=-2
Solve for x: (sqrt(5+\sqrt{24)})^x+(sqrt(5-\sqrt{24)})^x=10
The solution is x=2,x=-2