Question

Find the value of m if [2/3]^4+m× [2/3]^2+m =[2/3]^9-m​

Answer 1

[ 2 / 3 ] ⁴ + m × [ 2 / 3 ] ² + m = [ 2 / 3 ] ⁹ - m

16 / 81 + m × ( 2 / 3 ) ² + m = ( 2 / 3 ) ⁹ - m

16 / 81 + m × ( 4 / 9 ) + m = ( 2 / 3 ) ⁹ - m

16 / 81 + 13 / 9 m = ( 2 / 3 ) ⁹ - m

16 / 81 + 13 / 9 m = 512 / 19693 - m

16 / 81 + 13 / 9 m + m = 512 / 19693

16 / 81 + 22 / 9 m = 512 / 19683

22 / 9 m = 512 / 19683 - 16 / 81

22 / 9 m = 512 / 19683 - 3888 / 19683

22 / 9 m = 512 - 3888 / 19683

22 / m = - 3376 / 19683

m = - 3376 / 19683 × ( 9 / 22 )

m = - 3376 × 9 / 19683 × 22

m = - 30384 / 433026

m = - 1688 / 24057