Advertisements
Advertisements
प्रश्न
If `root(x)("a") = root(y)("b") = root(z)("c")` and abc = 1, prove that x + y + z = 0
Advertisements
उत्तर
Let `root(x)("a") = root(y)("b") = root(z)("c")`
⇒ `"a"^(1/x) = "k", "b"^(1/y) = "k", "c"^(1/z) = "k"`
⇒ a = k, b = k, c = k
It is also given that abc = 1
⇒ kx x ky x kz = 1
⇒ `"k"^(x + y + z)` = k°
⇒ x + y + z = 0.
APPEARS IN
संबंधित प्रश्न
If 5-P = 4-q = 20r, show that : `1/p + 1/q + 1/r = 0`
If `((a^-1b^2 )/(a^2b^-4))^7 ÷ (( a^3b^-5)/(a^-2b^3))^-5 = a^x . b^y` , find x + y.
If m = `root(3)(15) and n = root(3)(14), "find the value of " m - n - 1/[ m^2 + mn + n^2 ]`
Evaluate the following:
`(2^6 xx 5^-4 xx 3^-3 xx 4^2)/(8^3 xx 15^-3 xx 25^-1)`
Evaluate the following:
`(1 - 15/64)^(-1/2)`
Evaluate the following:
`16^(3/4) + 2(1/2)^-1 xx 3^0`
Solve for x:
`9 xx 3^x = (27)^(2x - 5)`
Solve for x:
9x+4 = 32 x (27)x+1
If x = `3^(2/3) + 3^(1/3)`, prove that x3 - 9x - 12 = 0
Find the value of (8p)p if 9p + 2 - 9p = 240.
