Advertisements
Advertisements
प्रश्न
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)`
Advertisements
उत्तर
∵ a, b, c, d are in proportion
`a/b = c/d` = k(say)
a = bk, c = dk.
L.H.S. = `(a^2 + ab + b^2)/(a^2 - ab + b^2)`
= `(b^2k^2 + bk.b + b^2)/(b^2k^2 - bk.b + b^2)`
= `(b^2(k^2 + k + 1))/(b^2(k^2 - k + 1)`
= `(k^2 + k + 1)/(k^2 - k + 1)`
R.H.S. = `(c^2 + cd + d^2)/(c^2 - cd + d^2)`
= `(d^2k^2 + dkd + d^2)/(d^2k^2 - dk.d + d^2)`
= `(d^2(k^2 + k + 1))/(d^2(k^2 - k + 1)`
= `(k^2 + k + 1)/(k^2 - k + 1)`
∴ L.H.S. = R.H.S.
APPEARS IN
संबंधित प्रश्न
Find the mean proportion of the following :
24 and 6
If 2x – 1, 5x – 6, 6x + 2 and 15x – 9 are in proportion, find the value of x.
Determine if the following ratio form a proportion:
200 mL : 2.5 L and Rs 4 : Rs 50
Show that the following numbers are in continued proportion:
16, 84, 441
Find the value of x if 5 : 3 : : x : 6.
4.5 g of an alloy of copper and zinc contains 3.5 g of copper. What weight of copper will there be in 18.9 g of the alloy?
Choose the correct statement:
Write the mean and extreme terms in the following ratios and check whether they are in proportion.
400 gm is to 50 gm and 25 rupees is to 625 rupees
Determine if the following are in proportion.
32, 48, 70, 210
If x + y + z = 0, the value of `x/(y + z)` is ______.
