Advertisements
Advertisements
Question
Show that:
`(x^(a-b))^(a+b)(x^(b-c))^(b+c)(x^(c-a))^(c+a)=1`
Advertisements
Solution
`(x^(a-b))^(a+b)(x^(b-c))^(b+c)(x^(c-a))^(c+a)=1`
LHS = `(x^(a-b))^(a+b)(x^(b-c))^(b+c)(x^(c-a))^(c+a)`
`=[x^((a-b)(a+b))][x^((b-c)(b+c))][x^((c-a)(c+a))]`
`=x^((a^2-b^2))x^((b^2-c^2))x^((c^2-a^2))`
`=x^(a^2-b^2+b^2-c^2+c^2-a^2)`
`=x^0`
= 1
= RHS
APPEARS IN
RELATED QUESTIONS
Simplify the following
`(4ab^2(-5ab^3))/(10a^2b^2)`
Solve the following equation for x:
`2^(3x-7)=256`
Assuming that x, y, z are positive real numbers, simplify the following:
`(sqrtx)^((-2)/3)sqrt(y^4)divsqrt(xy^((-1)/2))`
Simplify:
`(0.001)^(1/3)`
Show that:
`1/(1+x^(a-b))+1/(1+x^(b-a))=1`
Find the value of x in the following:
`2^(5x)div2x=root5(2^20)`
If `x = a^(m + n), y = a^(n + l)` and `z = a^(l + m),` prove that `x^my^nz^l = x^ny^lz^m`
If x is a positive real number and x2 = 2, then x3 =
Simplify:
`11^(1/2)/11^(1/4)`
Simplify:
`(9^(1/3) xx 27^(-1/2))/(3^(1/6) xx 3^(- 2/3))`
