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))`
Advertisements
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
Simplify the following:
`(5^(n+3)-6xx5^(n+1))/(9xx5^x-2^2xx5^n)`
Simplify:
`(0.001)^(1/3)`
Simplify:
`((25)^(3/2)xx(243)^(3/5))/((16)^(5/4)xx(8)^(4/3))`
Find the value of x in the following:
`5^(x-2)xx3^(2x-3)=135`
Solve the following equation:
`3^(x+1)=27xx3^4`
Solve the following equation:
`sqrt(a/b)=(b/a)^(1-2x),` where a and b are distinct primes.
State the quotient law of exponents.
Write the value of \[\sqrt[3]{125 \times 27}\].
If g = `t^(2/3) + 4t^(-1/2)`, what is the value of g when t = 64?
The simplest rationalising factor of \[\sqrt{3} + \sqrt{5}\] is ______.
