Question

If (x+4)is the mean proportional of (x-5)and (x-2) then find the value of x

Answer 1

If (x+4) is the mean proportional of (x-5) and (x-2)

${(x - 5)(x - 2)} = {(x + 4)}^{2} \\ {x}^{2} - 7x + 10 = {x}^{2} + 16 + 8x \\ 15x = - 6 \\ x = - \frac{6}{15} = - \frac{2}{5}$