Advertisements
Advertisements
प्रश्न
If a : b = c : d , then prove that `("a"^2 + "ab" +
"b"^2)/("a"^2 - "ab" + "b"^2) = ("c"^2 + "cd"+ "d"^2)/("c"^2 - "cd" + "d"^2)`
उत्तर
`"a"/"b" = "c"/"d" => "a" = "bc"/"d"`
LHS
`("a"^2 + "ab" + "b"^2)/("a"^2 - "ab" + "b"^2)`
`= (("bc"/"d")^2 + ("bc"/"d")"b" + "b"^2)/(("bc"/"d")^2 - ("bc"/"d")"b" + "b"^2)`
`= ("b"^2"c"^2 + "b"^2"cd" + "d"^2"b"^2)/("b"^2"c"^2 - "b"^2 "cd" + "d"^2"b"^2)`
`= ("b"^2("c"^2 + "cd" + "d"))/("b"^2("c"^2 - "cd" + "d"^2)) = ("c"^2 + "cd" + "d"^2)/("c"^2 - "cd" + "d"^2)` = RHS
LHS = RHS
Hence , proved.
APPEARS IN
संबंधित प्रश्न
If 7x – 15y = 4x + y, find the value of x : y. Hence, use componendo and dividendo to find the values of:
`(9x + 5y)/(9x - 5y)`
If `(x^2 + y^2)/(x^2 - y^2) = 2 1/8`, find: `(x^3 + y^3)/(x^3 - y^3)`
Given : x = `(sqrt(a^2 + b^2)+sqrt(a^2 - b^2))/(sqrt(a^2 + b^2)-sqrt(a^2 - b^2))`
Use componendo and dividendo to prove that `b^2 = (2a^2x)/(x^2 + 1)`.
Solve x : `(sqrt(36x + 1) + 6sqrt(x))/(sqrt(36x + 1) -6sqrt(x))` = 9
Find x from the following equations : `(sqrt(12x + 1) + sqrt(2x - 3))/(sqrt(12x + 1) - sqrt(2x - 3)) = (3)/(2)`
If `(x + y)/(ax + by) = (y + z)/(ay + bz) = (z + x)/(az + bx)`, prove that each of these ratio is equal to `(2)/(a + b)` unless x + y + z = 0
If x = `(2mab)/(a + b)`, find the value of `(x + ma)/(x - ma) + (x + mb)/(x - mb)`
If `(x^2 - 1)/(x^2 + 1) = 3/5`, the value of x is ______.
If a : b = 2 : 1, the value of (7a + 4b) : (5a – 2b) is ______.
If `x/(a + b - c) = y/(b + c - a) = z/(c + a - b) = 5` and a + b + c = 7; the value of x + y + z is ______.
