Question

Solve bythi quadratic equation​

Answer 1

Answer:

x=3

Step-by-step explanation:

1 method :-

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

2 method :-

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

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