Advertisements
Advertisements
प्रश्न
Using properties of proportion, solve for x:
`(sqrt(x + 1) + sqrt(x - 1))/(sqrt(x + 1) - sqrt(x - 1)) = (4x - 1)/2`
उत्तर
`(sqrt(x + 1) + sqrt(x - 1))/(sqrt(x + 1) - sqrt(x - 1)) = (4x - 1)/2`
Applying componendo and dividendo,
`(sqrt(x + 1) + sqrt(x - 1) + sqrt(x + 1) - sqrt(x - 1))/(sqrt(x + 1) + sqrt(x - 1) - sqrt(x + 1) + sqrt(x - 1)) = (4x - 1 + 2)/(4x - 1 - 2)`
`(2sqrt(x + 1))/(2sqrt(x - 1)) = (4x + 1)/(4x - 3 )`
Squaring both sides,
`(x + 1)/(x - 1) = (16x^2 + 1 + 8x )/(16x^2 + 9 - 24x)`
Applying componendo and dividendo,
`(x + 1 + x - 1)/(x + 1 - x + 1) = (16x^2 + 1 + 8x + 16x^2 + 9 - 24x)/(16x^2 + 1 + 8x - 16x^2 - 9 + 24x)`
`(2x)/2 = (32x^2 + 10 - 16x )/(32x - 8)`
`x = (16x^2 + 5 - 8x)/(16x - 4)`
16x2 – 4x = 16x2 + 5 – 8x
4x = 5
`x = 5/4`
APPEARS IN
संबंधित प्रश्न
If p + r = mq and `1/q + 1/s = m/r`; then prove that p : q = r : s.
Given, `x/(b - c ) = y/(c - a ) = z/(a - b)` , Prove that
ax+ by + cz = 0
Find the value of the unknown in the following proportion :
5 : 12 :: 15 : x
Find the fourth proportion to the following:
(p2q - qr2 ), (pqr - pr2 ) and (pq2 - pr2)
Find two nurnbers whose mean proportional is 12 and the third proportional is 324.
If a, b, c, d are in continued proportion, prove that:
(a2 + b2 + c2) (b2 + c2 + d2) = (ab + bc + cd)2.
Write (T) for true and (F) for false in case of the following:
51 : 68 : : 85 : 102
If a, b, c, d, e are in continued proportion, prove that: a : e = a4 : b4.
Which of the following ratios are in proportion?
Determine if the following ratios form a proportion. Also, write the middle terms and extreme terms where the ratios form a proportion.
39 litres : 65 litres and 6 bottles : 10 bottles
