Question

show that :(x^a+b/x^c)^a-b×(x^b+c/x^a)^b-c×(x^c+a/x^b)^c-a=1​

Answer 1

Solution -

To show : = 1

Let us simplify the LHS first

> ( x^a+b/x^c)^a-b × (x^b+c/x^a)^b-c × (x^c+a/x^b)^c-a

> [ x^{a+b-c}]^(a-b) × [x^{b+c-a}]^(b-c) × [x^(c+a-b)]^(c-a)

> x^ [ (a+b-c)(a-b) ] × x^[ (b+c-a)(b-c)] × x^[ (c+a-b)(c-a)]

> x^[a² + ab - ac - ab - b² + bc ] × x^[ b² + bc - ab - bc - c² + ac] × x^[ c² + ac - bc - ac - a² + ab]

> x^[ a² + ab - ac - ab - b² + bc +b² + bc - ab - bc - c² + ac + c² + ac - bc - ac - a² + ab ]

> x^0

> 1

Hence Shown