Find all Real solutions to this equation: (x - 2)(9x^2 - 8x)=(x - 2)(16x - 16)

Jaylyn Horne 2022-10-26 Answered
Find all Real solutions to this equation:
( x 2 ) ( 9 × 2 8 x ) = ( x 2 ) ( 16 x 16 )
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Answers (1)

toliwask
Answered 2022-10-27 Author has 15 answers
( x 2 ) ( 9 × 2 8 x ) = ( x 2 ) ( 16 x 16 ) 9 x 3 26 x 2 + 16 x = 16 x 2 48 x + 32
Subtract 16 x 2 48 x + 32 from both sides
9 x 3 26 x 2 + 16 x 16 x 2 + 48 x 32 = 0 9 x 3 42 x 2 + 64 x 32 = 0
One factor of this polynomial is x-2
Divide the polynomial 9 x 3 42 x 2 + 64 x 32 by x-2. So we get:
( 9 x 3 42 x 2 + 64 x 32 ) / ( x 2 ) = 9 x 2 24 x + 16
Our polynomial becomes:
( 9 x 2 24 x + 16 ) = ( 3 x 4 ) 2 ( x 2 ) ( 3 x 4 ) 2 = 0
see factors equal to 0
x-2=0 or 3x-4=0
x=2 or x=4/3
Real solutions are x=2, 4/3
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