CAT 2020 Exam Shift 2 Solved Paper

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Question : 71 of 76

Marks: +1, -0

The number of integers that satisfy the equality

(x^{2}-5 x+7)^{x+1}=1

is

2
3
5
4

Solution:

(x^{2}-5 x+7)^{x+1}=1

We know, for

a^{b}=1

, if

-a=-1

then

b

is even.

-a=1

then

b

is any number

-a>0

then

b=0

Case 1:

x+1=0 ⇒ x=-1

Case 2:

x^{2}-5 x+7=1 ⇒ x^{2}-5 x+6=0 ⇒ x=2

or 3
Case 3:

x^{2}-5 x+7=-1 ⇒ x^{2}-5 x+8=0

∴

The number of integers satisfies the equation is 3

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