Question

( x - 1)⅔ =25 please tell me the solution of this question

Answer 1

Solution:

${(x - 1)}^{ \frac{2}{3} } = 25$
taking power 3/2 both sides

${(x - 1)}^{ \frac{2 \times 3}{3 \times 2} } = {(25)}^{ \frac{3}{2} } \\ \\ x - 1 = {5}^{2 \times \frac{3}{2} } \\ \\ x - 1 = {5}^{3} \\ \\ x - 1 = 125 \\ x = 125 + 1 \\ \\ x = 126$
Hope it helps you.

Answer 2

Given,

$(x-1)^{\frac{2}{3}}=25\\\\Using,\;\;a^{n}=b\implies\;a=b^{\frac{1}{n}}\\\\(x-1)=25^{\frac{3}{2}}\\\\x-1=\sqrt{25^{3}}\\\\x-1=\sqrt{25\times25\times25}\\\\x-1=\sqrt{5^{2}\times5^{2}\times5^{2}}\\\\x-1=\sqrt{5^{2+2+2}}\\\\x-1=\sqrt{5^{6}}\\\\x-1=\pm5^{3}\\\\x-1=\pm125\\\\\textbf{Taking +ve}\\\\x-1=125\\\\x=125+1\\\\x=126\\\\\\\textbf{Taking -ve}\\\\x-1=-125\\\\x=-125+1\\\\x=-124$

Hence,

x = 126 or  x = -124