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Question

Solve the following equation:
3x+63x=95x

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Solution

3x+63x=95x
squaring both sides, we get
3x+363x+2×6×3x×13x=95x
3x+363x+12=95x
(3x)2+36+12(3x)=(95x)(3x)
x2+96x+36+3612x=2715x9x+5x2
x218x+81=24x+5x2=27
5x2x224x+18x+2781=0
4x26x54=0
2x23x27=0
x=3±94×2×272×2
x=3±2254 3±2254
x=3+154 x=3152
x=184=92 x=122=6
x=6,92
Hence, solved.






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