Question

I (x-14)³+(x-15)³+(x-16)³ = 3(x-14)(x-15)(x-16), Then x = ?​

Answer 1

Answer:

$\mathrm{\left(x-14\right)^3+\left(x-15\right)^3+\left(x-16\right)^3=3\left(x-14\right)\left(x-15\right)\left(x-16\right)\quad :\quad x=15}$

Step-by-step explanation:

$\mathrm{\left(x-14\right)^3+\left(x-15\right)^3+\left(x-16\right)^3=3\left(x-14\right)\left(x-15\right)\left(x-16\right)}$

$\mathrm{3x^3-135x^2+2031x-10215=3\left(x^2-29x+210\right)\left(x-16\right)}$

$\mathrm{3x^3-135x^2+2031x-10215=3\left(x^3-45x^2+674x-3360\right)}$

$\mathrm{3x^3-135x^2+2031x-10215=3x^3-135x^2+2022x-10080}$

$\mathrm{3x^3-135x^2+2031x-10215=3x^3-135x^2+2022x-10080}$

$\mathrm{Add\:}10215\mathrm{\:to\:both\:sides}$

$\mathrm{3x^3-135x^2+2031x-10215+10215=3x^3-135x^2+2022x-10080+10215}$

$\mathrm{3x^3-135x^2+2031x=3x^3-135x^2+2022x+135}$

$\mathrm{Subtract\:3x^3-135x^2+2022x}\mathrm{\:from\:both\:sides}$

$\mathrm{3x^3-135x^2+2031x-\left(3x^3-135x^2+2022x\right)}$

$=\mathrm{3x^3-135x^2+2022x+135-\left(3x^3-135x^2+2022x\right)}$

$9x=135$

$\mathrm{Divide\:both\:sides\:by\:}9$

$\mathrm{\frac{9x}{9}=\frac{135}{9}}$

$x=15$