Question

solve please urgent need ​

Answer 1

$GOOD \: \: MORNING \: \\ \\ 4 {}^{(x + 1)} + 4 {}^{(1 - x)} = 10 \\ \\ 4 {}^{x} \times 4 + 4 {}^{} \times 4 {}^{( - x)} = 10 \\ \\ let \: \: 4 {}^{x} = z \\ \\ 4z {}^{2} + 4 = 10z \\ \\ 4z {}^{2} - 10z + 4 = 0 \\ \\ 2z {}^{2} - 5z + 2 = 0 \\ \\ 2z {}^{2} - 4z - 1z + 2 = 0 \\ \\ 2z(z -2 ) - 1(z - 2) = 0 \\ \\ (2z - 1) = 0 \: \: \: \: or \: \: \: \: (z - 2) = 0 \\ \\ z = 1 \div 2 \: \: \: \: or \: \: \: z = 2 \\ \\ 4 {}^{x} = 2 {}^{ - 1} \: \: \: or \: \: \: 4 {}^{x} = 2 {}^{1} \\ \\ 2 {}^{2x} = 2 {}^{ - 1} \: \: \: or \: \: \: 2 {}^{2x} = 2 {}^{1} \\ \\ now \: compare \: \: powers \: of \: 2 \: we \: have \\ \\ 2x = - 1 \: \: \: or \: \: \: 2x = 1 \\ \\ x = - 1 \div 2 \: \: \: or \: \: \: x = 1 \div 2 \\ \\ therefore \: \: \: x = - 1 \div 2 \: \: \: \: or \: \: \: \: x = 1 \div 2$