Advertisements
Advertisements
प्रश्न
If ax = by = cz and b2 = ac, prove that y = `(2xz)/(z + x)`
Advertisements
उत्तर
Let ax = by = cz = k
⇒ `"a" = "k"^(1/x), "b" = "k"^(1/y), "c" = "k"^(1/2)`
It is also given that b2 = ac
⇒ `"k"^(2/y) = "k"^(1/x) xx "k"^(1/2)`
⇒ `"k"^(2/y) = "k"^(1/x + 1/z)`
⇒ `(2)/y = (1)/x + (1)/z`
⇒ y = `(2zx)/(z + x)`.
APPEARS IN
संबंधित प्रश्न
Find x, if : `sqrt( 2^( x + 3 )) = 16`
Solve for x:
`2^(3x + 3) = 2^(3x + 1) + 48`
If ax = by = cz and b2 = ac, prove that: y = `[2xz]/[x + z]`
Evaluate the following:
`(4^3 xx 3^7 xx 5^6)/(5^8 xx 2^7 xx 3^3)`
Evaluate the following:
`(27)^(2/3) xx 8^((-1)/6) ÷ 18^((-1)/2)`
Solve for x:
9 x 81x = `(1)/(27^(x - 3)`
Solve for x:
5x2 : 5x = 25 : 1
Find the value of k in each of the following:
`(1/3)^-4 ÷ 9^((-1)/(3)` = 3k
Find the value of 'a' and 'b' if:
92a = `(root(3)(81))^(-6/"b") = (sqrt(27))^2`
Prove the following:
`(x^("a"+"b")/x^"c")^("a"-"b") · (x^("c"+"a")/(x^"b"))^("c"-"a") · ((x^("b"+"c"))/(x"a"))^("b"-"c")` = 1
