Advertisements
Advertisements
प्रश्न
Using the properties of proportion solve for x given `(x^4 + 1)/(2x^2) = 17/8`
उत्तर
`(x^4 + 1)/(2x^2) = 17/8`
Applying componendo and dividendo we get
`(x^4 + 1 + 2x^2)/(x^4 + 1 - 2x^2) = (17 + 8)/(17 - 8)`
`=> ((x^2)^2 + (1)^2 + 2 xx x^2 + 1)/((x^2)^2 + (1)^2 - 2 xx x^2 xx 1) = 25/9`
`=> (x^2 + 1)^2/(x^2 - 1)^2 = 5^2/3^2`
`=> ((x^2 + 1)/(x^2 - 1))^2 = (5/3)^2`
`=> (x^2 + 1)/(x^2 - 1) = 5/3`
Applying componeddo and diividendo we get
`(x^2 + 1 + x^2 - 1)/(x^2 + 1 - x^2 + 1) = (5 + 3)/(5 - 3)`
`=> (2x^2)/2 = 8/2`
`=> x^2 = 4`
`=> x = +- 2`
APPEARS IN
संबंधित प्रश्न
If `x = (sqrt(m + n) + sqrt(m - n))/(sqrt(m + n) - sqrt(m - n))`, express n in terms of x and m.
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)
If a : b =c : d, then prove that `("a"^2 + "c"^2)/("b"^2 + "d"^2) = ("ac")/("bc")`
Solve for x : `(1 - px)/(1 + px) = sqrt((1 + qx)/(1 - qx)`
If `p/q = r/s`, prove that `(2p + 3q)/(2p - 3q) = (2r + 3s)/(2r - 3s)`.
if `(3a + 4b)/(3c + 4d) = (3a - 4b)/(3c - 4d)` Prove that `a/b = c/d`.
If a : b : : c : d, prove that (2a + 3b)(2c – 3d) = (2a – 3b)(2c + 3d)
If `(5x + 7y)/(5u + 7v) = (5x - 7y)/(5u - 7v)`, show that `x/y = u/v`
Find x from the following equations : `(sqrt(a + x) + sqrt(a - x))/(sqrt(a + x) - sqrt(a - x)) = c/d`
Given that `(a^3 + 3ab^2)/(b^3 + 3a^2b) = (63)/(62)`. Using componendo and dividendo find a: b.
