Question

The roots of the equation 2 2x ​-10.2 x +16=0 are (A)1,3 (B)2,4 (C) 2,3 (D) none of these

Answer 1

2²ˣ-10.2ˣ+16=0
or, (2ˣ)²-10.2ˣ+16=0
Let, 2ˣ=a
∴, a²-10a+16=0
or, a²-8a-2a+16=0
or, a(a-8)-2(a-8)=0
or, (a-8)(a-2)=0
∴, either, a-8=0
or, a=8
or, 2ˣ=8
or, 2ˣ=2³
or, x=3
Or, a-2=0
or, a=2
or, 2ˣ=2
or, 2ˣ=2¹
or, x=1
∴, Roots of the given equation are: (A) 1,3