$\left(\dfrac{x^{b}}{x^{c}}\right)^{b+c-a}.\left(\dfrac{x^{c}}{x^{a}}\right)^{c+a-b}.\left(\dfrac{x^{a}}{x^{b}}\right)^{a+b-c}=?$
xabc
1
xab + bc + ca
xa + b + c
Explanation:
Given Exp.
= x(b - c)(b + c - a) . x(c - a)(c + a - b) . x(a - b)(a + b - c)
= x(b - c)(b + c) - a(b - c) . x(c - a)(c + a) - b(c - a) . x(a - b)(a + b) - c(a - b)
= x(b2 - c2 + c2 - a2 + a2 - b2) . x-a(b - c) - b(c - a) - c(a - b)
= (x0 x x0)
= (1 x 1) = 1.
Given Exp.
= x(b - c)(b + c - a) . x(c - a)(c + a - b) . x(a - b)(a + b - c)
= x(b - c)(b + c) - a(b - c) . x(c - a)(c + a) - b(c - a) . x(a - b)(a + b) - c(a - b)
= x(b2 - c2 + c2 - a2 + a2 - b2) . x-a(b - c) - b(c - a) - c(a - b)
= (x0 x x0)
= (1 x 1) = 1.