Question

${2}^{x} + {5}^{x} = {10}^{x}$
find values of x satisfying this equation .​

Answer 1

Answer:

sin

−1

cos(

x

2

+5x+3

2x

2

+10x+4

)=cot(cot

−1

(

9x

2−18x

))+

2

π

⇒sin

−1

sin(

2

π

−(

x

2

+5x+3

2x

2

+10x+4

))=

9x

2−18x

+

2

π

⇒

2

π

−

x

2

+5x+3

2x

2

+10x+4

=

9x

2−18x

+

2

π

⇒−18x

3

−90x

2

−36x=2x

2

+10x+6−18x

3

−90x−54x

⇒2x

2

−8x+6=0⇒x

2

−4+3=0⇒(x−1)(x−3)=0

Therefore product of roots is 1×3=3

Answer verified by Toppr

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Study later

View solution

2tan

−1

(

1−x

1+x

)+sin

−1

(

1+x

2

1−x

2

)= 3