Advertisements
Advertisements
प्रश्न
Show that:
`(x^(a^2+b^2)/x^(ab))^(a+b)(x^(b^2+c^2)/x^(bc))^(b+c)(x^(c^2+a^2)/x^(ac))^(a+c)=x^(2(a^3+b^3+c^3))`
उत्तर
`(x^(a^2+b^2)/x^(ab))^(a+b)(x^(b^2+c^2)/x^(bc))^(b+c)(x^(c^2+a^2)/x^(ac))^(a+c)=x^(2(a^3+b^3+c^3))`
LHS = `(x^(a^2+b^2)/x^(ab))^(a+b)(x^(b^2+c^2)/x^(bc))^(b+c)(x^(c^2+a^2)/x^(ac))^(a+c)`
`=(x^(a^2+b^2-ab))^(a+b)(x^(b^2+c^2-bc))^(b+c)(x^(c^2+a^2-ac))^(a+c)`
`=[x^((a+b)(a^2+b^2-ab))][x^((b+c)(b^2+c^2-bc))][x^((a+c)(c^2+a^2-ac))]`
`=(x^(a^3+b^3))(x^(b^3+c^3))(x^(a^3+c^3))`
`=x^(2(a^3+b^3+c^3))`
= RHS
APPEARS IN
संबंधित प्रश्न
Prove that:
`(x^a/x^b)^(a^2+ab+b^2)xx(x^b/x^c)^(b^2+bc+c^2)xx(x^c/x^a)^(c^2+ca+a^2)=1`
If abc = 1, show that `1/(1+a+b^-1)+1/(1+b+c^-1)+1/(1+c+a^-1)=1`
If 49392 = a4b2c3, find the values of a, b and c, where a, b and c are different positive primes.
Show that:
`(x^(a-b))^(a+b)(x^(b-c))^(b+c)(x^(c-a))^(c+a)=1`
Find the value of x in the following:
`5^(x-2)xx3^(2x-3)=135`
Find the value of x in the following:
`(root3 4)^(2x+1/2)=1/32`
Solve the following equation:
`4^(2x)=(root3 16)^(-6/y)=(sqrt8)^2`
Write \[\left( \frac{1}{9} \right)^{- 1/2} \times (64 )^{- 1/3}\] as a rational number.
If \[\sqrt{2} = 1 . 4142\] then \[\sqrt{\frac{\sqrt{2} - 1}{\sqrt{2} + 1}}\] is equal to
Find:-
`32^(1/5)`
