The sum of all distinct real values of x that satisfy the equation $10^x + \cfrac{4}{10^x} = \cfrac{81}{2}$ , is
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Question

The sum of all distinct real values of x that satisfy the equation $$10^x + \cfrac{4}{10^x} = \cfrac{81}{2}$$, is

Accepted Answer

2 log ⁡ 10 2 2 \log_{10}2 2 lo g 10 ​ 2. Taking 10 x = a 10^x=a 1 0 x = a we get a + 4 a = 81 2 a+\frac{4}{a}=\frac{81}{2} a + a 4 ​ = 2 81 ​ This would give the quadratic equation: 2 a 2 − 81 a + 8 = 0 2a^2-81a+8=0 2 a 2 − 81 a + 8 = 0 We want to find the sum of possible values of x, let the value of x be x1 and x2 these would correspond

The sum of all distinct real values of x that satisfy the equation 10x+410x=81210^x + \cfrac{4}{10^x} = \cfrac{81}{2}10x+10x4​=281​, is

The sum of all distinct real values of x that satisfy the equation 10x+410x=81210^x + \cfrac{4}{10^x} = \cfrac{81}{2}10x+10x4​=281​, is

The sum of all distinct real values of x that satisfy the equation $10^x + \cfrac{4}{10^x} = \cfrac{81}{2}$ , is

The sum of all distinct real values of x that satisfy the equation $10^x + \cfrac{4}{10^x} = \cfrac{81}{2}$ , is