Question

√x²-1 + (x²-11x+10)² + (x²-9x+8)^4 = 0

Answer 1

Answer:

x=1 is the only root

put and check

or

see factors ,first term x-1 is factor of it

factorise second term x-1 is its factor

factorise third term x-1 is also its factor now

main question will arise in you how you are sure there is no further answers except x=1

see

root is always a positive quantity

so first term is positive or equal to zero

now squares or even power quantities are always positive or zero so second and third term is also positive

so there sum will only be zero if all three quantities are simultaneously equal to zero for same x

now root quantitu is zero for x=1 and -1

second term is zero for x= 10 and 1

third quantiy is zero for x= 1 and 8

so commom value of x for which all three are simultaneously zero is x=1

hence there is only one real solution to this question that is x=1

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