Advertisements
Advertisements
प्रश्न
Using the properties of proportion, solve for x, given `(x^4 + 1)/(2x^2) = 17/8`.
Advertisements
उत्तर
`(x^4 + 1)/(2x^2) = 17/8`
Using componendo and dividendo,
If `a/b = c/d`
`(x^4 + 1 + 2x^2)/(x^4 + 1 - 2x^2) = (17 + 8)/(17 - 8)`
`=> (x^2 + 1)^2/(x^2 - 1)^2 = 25/9`
`=> ((x^2 + 1)/(x^2 - 1)) = (5/3)^2`
`=> (x^2 + 1)/(x^2 - 1) = 5/3`
⇒ 3(x2 + 1) = 5(x2 − 1)
⇒ 3x2 + 3 = 5x2 − 5
5x2 − 3x2 = 3 + 5
2x2 = 8
x2 = 4
x = `+- sqrt4`
x = ± 2
APPEARS IN
संबंधित प्रश्न
Given four quantities a, b, c and d are in proportion. Show that: (a – c)b2 : (b – d)cd = (a2 – b2 – ab) : (c2 – d2 – cd)
If `x/a = y/b = z/c` prove that `(2x^3 - 3y^3 + 4z^3)/(2a^3 - 3b^3 + 4c^3) = ((2x - 3y + 4z)/(2a - 3b + 4c))^3`
If a, b, c, d are in continued proportion, prove that (b − c)2 + (c − a)2 + (d − b)2 = (d − a)2.
Find the value of x in the following proportions : 2.5 : 1.5 = x : 3
Write (T) for true and (F) for false in case of the following:
81 kg : 45 kg : : 18 men : 10 men
The 1st, 3rd, and 4th terms of a proportion are 12, 8, and 14 respectively. Find the 2nd term.
If the cost of 12 pens is Rs 138, then the cost of 14 such pens is
If a, b, c and d are in proportion, prove that: `(a^2 + ab + b^2)/(a^2 - ab + b^2) = (c^2 + cd + d^2)/(c^2 - cd + d^2)`
If a, b, c are in continued proportion, prove that: a2 b2 c2 (a-4 + b-4 + c-4) = b-2(a4 + b4 + c4)
If 2, 6, p, 54 and q are in continued proportion, find the values of p and q.
