Advertisements
Advertisements
प्रश्न
Prove that : `((x^a)/(x^b))^( a + b - c ) (( x^b)/(x^c))^( b + c - a )((x^c)/(x^a))^( c + a - b)`
Advertisements
उत्तर
LHS = `((x^a)/(x^b))^( a + b - c ) (( x^b)/(x^c))^( b + c - a )((x^c)/(x^a))^( c + a - b)`
= `(x^(a - b))^( a + b - c) xx (x^(b - c))^( b + c - a ) xx ( x^(c - a ))^( c + a - b)`
= `x^[( a - b )( a + b - c )] xx x^[( b - c )( b + c - a )] xx x^[( c - a )(c + a - b)]`
= `x^( a^2 + ab - ac - ab - b^2 + bc) xx x^(b^2 + bc - ab - cd - c^2 + ac) xx x^( c^2 + ac - bc - ac - a^2 + ab )`
= `x^(a^2 - ac - b^2 + bc + b^2 - ab - c^2 + ac + c^2 - bc - a^2 + ab )`
= x0
= 1
= RHS
APPEARS IN
संबंधित प्रश्न
Solve:
22x + 2x+2 − 4 × 23 = 0
Solve for x : (a3x + 5)2. (ax)4 = a8x + 12
Solve for x:
`2^(3x + 3) = 2^(3x + 1) + 48`
If 4x + 3 = 112 + 8 × 4x, find the value of (18x)3x.
If 5x + 1 = 25x - 2, find the value of 3x - 3 × 23 - x.
Evaluate the following:
`(12^2 xx 75^-2 xx 35 xx 400)/(48^2 xx 15^-3 xx 525)`
Evaluate the following:
`sqrt(1/4) + (0.01)^(-1/2) - (27)^(2/3)`
Solve for x:
`sqrt((3/5)^(x + 3)) = (27^-1)/(125^-1)`
Find the value of 'a' and 'b' if:
92a = `(root(3)(81))^(-6/"b") = (sqrt(27))^2`
Prove the following:
`(x^("p"("q"-"r")))/(x^("q"("p"-"r"))) ÷ (x^"q"/x^"p")^"r"` = 1
