Solve for the following equation 5^(2x)-5^(x+3)+125=5^x

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07 Jun 2013 Equation

Solve for the following equation
5^(2x)-5^(x+3)+125=5^x

OPtion

1) x=1, x=2
2) x=2, x=0
3) x=3, x=1
4) x=3, x=2
5) x=3, x=4
6) x=5, x=1
7) x=3, x=0
8) x=1, x=0
9) x=4, x=5
10) None of these

Solution

Let 5^x=k
k^2-k.5^3+125=k
k^2-126k+125=0
solve
k=125 or k=1
5^x=125 or 5^x=1
5^x=5^3 or 5^x=5^0
x=3, x=0
option 7

Correct Option: 7 Best Solution (11)

Dr.Dipin Singh   11 years AGO

5^(2x)-5^(x+3)+125=5^x

suppose 5^x=y ,
then eqn 5^(2x)-5^(x+3)+125=5^x

becomes
y^2-125y+125=y
y^2-126y+125=0
y=125,1
so 5^x=125 = 5^3 or 5^x=1 = 5^0
so x=3 or x=0 .. option 7

Like? Yes (15) | No (5)  

Nilesh   11 years AGO

x=3, x=0
when
x=3,
5^(2x)-5^(x+3)+125=5^x or 5^6 -5^6+125= 5^3
or 125=125 .. LHS=RHS
also when x=0,
5^(2x)-5^(x+3)+125=5^x or 5^0-5^3 +125= 5^0
1=1 .. LHS=RHS

Like? Yes (5) | No (1)  

saisaranya   11 years AGO

let a=5^x then according to the question a^2-126a+125 roots are 125 and 1 then x=0,3

Like? Yes (2) | No   

Himank Agrawal   11 years AGO

Given equation
5^(2x)-5^(x+3)+125=5^x
Let 5^x=y
y^2-(5^3)*y+125=y
y^2-125y+125=y
y^2-126y+125=0
solving above quadratic eqn in y we get
y=1 and y=125
5^x=1 and 5^x=125
So the required values of x are x=0 and x=3

Like? Yes (3) | No (2)  

ganesh   11 years AGO

In above potions, only 7th one is possible

Like? Yes (2) | No (1)  

Devendra Marghade   11 years AGO

5^(2x)-5^(x+3)+125=5^x
If 5^x=y, then above eqn. becomes y^2-126y+125=0
or (y-125)(y-1)=0
y =125 => x = 3
or y=1 => x = 0

Like? Yes (2) | No (1)  

Vinay Sipani    11 years AGO

5^x = t

=> t^2 - 125t + 125 = t
=> t^2 - 126t + 125 = 0
=> t = 1,125

=> x = log(t)/log(5)
=> x = 0,3

Like? Yes (3) | No (3)  

Adarsha Upadhya   11 years AGO

5^(2x)-5^(x+3)+125=5^x
5^(2x)-5^(x+3)-5^x=5^3
on solving we get
x=3 or x=0

Like? Yes (6) | No (6)  

Vibhu arya   11 years AGO

let 5^ x be y

5^2 x = y^2

5^ (x+3) = 125 * 5^x = 125 y

so we get y^2 - 125 y + 125 = y

or y^2 - 125 y - y + 125 = 0

or (y-125)(y-1) = 0

y = 125 => x = 3

or y= 1 => x = 0

so x = { 0, 3 }

Like? Yes (2) | No (2)  

Gotlooru Venkata Kartheek Kumar   11 years AGO

By substitution,
We get the answer

Like? Yes (2) | No (2)  

vinod   11 years AGO

verify options

Like? Yes (1) | No (2)