Solve: 5 x+1 + 5 2−x =126 .

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Solve: $5 x + 1 + 5 2 − x = 126$ .

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2, -1

2, -3

2, -4

2, 0

answer is A.

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Detailed Solution

Given,

5 x + 1 + 5 2 − x = 126

.
We know that formula for

a x 2 + b x + c = 0,

x = − b ± b 2 − 4 a c 2 a

.
Finding the value of the coefficients,

5 x + 1 + 5 2 − x = 126 ⇒ 5 x × 5 + 52 5 x = 126 ⇒ 5 2 x × 5 + 25 = 126 × 5 x

Consider

5 x = y

.
So, the above equation becomes,

5 y 2 − 126 y + 25 = 0 a = 5, b = − 126, c = 25

y = − b ± b 2 − 4 a c 2 a ⇒ y = − − 126 ± − 126 2 − 4 × 5 × 25 2 × 5 ⇒ y = 126 ± 124 10 ⇒ y = 25, 0.2

As we considered

5 x = y

, then the value of x is,
If y=25,

5 x = 25 ⇒ 5 x = 52 ⇒ x = 2

If y=0.2,

5 x = 0.2 ⇒ 5 x = 5 − 1 ⇒ x = − 1

The values of x for the equation are 2, -1.
The correct option is 1).

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