How many values work?

Algebra Level 2

Find the product of all values of $x$ that satisfy the equation:

$x^{x^{2}-25}=1$

The answer is 25.

6 solutions

Muralidhar Kamidi
Feb 18, 2014

Only possible values of x I could see were:

5 and -5, making the exponent zero and hence value of the expression LHS 1.
1 and -1, raising each of them to power -24 and hence making its value 1 again.
multiplying them gives 5.

No, $5 \times -5 \times -1 \times 1=25$ .

Finn Hulse - 7 years, 3 months ago

x x-25=i give x=5,-5 and 1 & -1 also satisfies the equation. so the result is (-5 5 1 (-1) )=25

Mabud Ali Sarkar - 7 years, 3 months ago

thn answer should be 5 as 5 is the value of x , 25 is the value of x^2 to make the power 0

Sumit Pehal - 6 years, 10 months ago

Tanmoy Guha
Feb 27, 2014

(x^2-25)*logx = log1 => (x^2-25)=0 ,
Hence, x=5, -5. Also, it is valid for x=1, -1, so, 5.-5.1.-1 = 25.

Akshita Khandelwal
Feb 22, 2014

take log with base x on both sides. on solving it will become x.x=25

Eslam El-Deeb
Feb 17, 2014

1) the same power so x = 1 2) let 1 = x^0 so x^2 -25 = 0 so x equal 5 and -5 3) by powering the both sides by (-1) it will be x^(25-x^2) = 1 so in this case x can be equal -1 bexause the power will be even

Fahim Rahman
Feb 14, 2014

x^0 = 1 so, x^2 - 25 should be 0 then, x = 5, -5

if x =1, then 1^n = 1 so, x = 1, -1 The product of x is = -1 * 1 * -5 * 5 = 25

how x= -1 ?! :/

Nur Uddin - 7 years, 3 months ago

if x = -1 then x^2-25 =-24 LHS = (-1)^-24 = 1 = RHS

Fahim Rahman - 7 years, 3 months ago

if x= -1 then, it should be, x^2-25 = -24. now, LHS=> (-1)^-24 = 1= RHS

Nur Uddin - 7 years, 3 months ago

Vishnudatt Gupta
May 13, 2014

firstly factorize power and equate to 0& 1

(x-5)(x+5)=0

x=-5,5

(x-5)(x+5)=1

x=26^1/2 & this will not satisfy the equation

now to x=1 and see the values

x=1,-1

so product is 5 -5 1*-1=25

How many values work?

The answer is 25.

6 solutions

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