Advertisements
Advertisements
प्रश्न
If a, b, c and d are in proportion, prove that: `(a^2 + b^2)/(c^2 + d^2) = "ab + ad - bc"/"bc + cd - ad"`
Advertisements
उत्तर
∵ a, b, c, d are in proportion
`a/b = c/d` = k(say)
a = bk, c = dk.
L.H.S. = `(a^2 + b^2)/(c^2 + d^2)`
= `(b^2k^2 + b^2)/(d^2k^2 + d^2)`
= `(b^2(k^2 + 1))/(d^2(k^2 + 1)`
= `b^2/d^2`
R.H.S. = `"ab + ad - bc"/"bc + cd - ad"`
= `"bk.b + bk.d - b.dk"/"b.kd + dk.d - bk.d"`
= `(k(b^2 + bd - bd))/(k(bd + d^2 - bd)`
= `b^2/d^2`
∴ L.H.S. = R.H.S.
APPEARS IN
संबंधित प्रश्न
Using properties of proportion, solve for x. Given that x is positive:
`(2x + sqrt(4x^2 -1))/(2x - sqrt(4x^2 - 1)) = 4`
Find the third proportional to a – b and a2 – b2
What number must be added to each of the number 16, 26 and 40 so that the resulting numbers may be in continued proportion?
Find the value of x in the following proportions : 3 : x = 24 : 2
Determine if the following ratio form a proportion:
25 cm : 1 m and Rs 40 : Rs 160
If the cost of 12 pens is Rs 138, then the cost of 14 such pens is
If `x/a = y/b = z/c`, prove that `[(a^2x^2 + b^2y^2 + c^2z^2)/(a^2x + b^3y +c^3z)]^3 = "xyz"/"abc"`
Write the mean and extreme terms in the following ratios and check whether they are in proportion.
78 litre is to 130 litre and 12 bottles is to 20 bottles
Find the missing number in the box in the proportion:
`8/square = 3.2/4`
If 2x, 9 and 18 are in continued proportion, the value of x is ______.
