Advertisements
Advertisements
प्रश्न
If a, b, c and d are in proportion, prove that: (5a + 7b) (2c – 3d) = (5c + 7d) (2a – 3b).
Advertisements
उत्तर
It is given that
a, b, c, d are in proportion
Consider `a/b = c/d = k`
a = bk, c = dk
LHS = (5a + 7b)(2c – 3d)
LHS = (5bk + 7b)(2dk – 3d) ...[Substituting the values]
LHS = b(5k + 7) d(2k – 3) ...[Taking out the common terms]
LHS = bd (5k + 7)(2k - 3)
LHS = bd [5k (2k - 3) + 7(2k - 3)]
LHS = bd (10k2 - 15k + 14k - 21)
LHS = bd (10k2 - k - 21) ... (I)
RHS = (5c + 7d)(2a – 3b)
RHS = (5dk + 7d)(2bk – 3b) ...[Substituting the values]
RHS = d(5k + 7) b(2k – 3) ...[Taking out the common terms]
RHS = bd (5k + 7)(2k – 3)
RHS = bd [5k(2k - 3) + 7(2k - 3)]
RHS = bd (10k2 - 15k + 14k - 21)
LHS = bd (10k2 - k - 21) ... (II)
From (I) and (II),
Therefore, LHS = RHS.
APPEARS IN
संबंधित प्रश्न
Find the third proportional to a – b and a2 – b2
Check whether the following numbers are in continued proportion.
3, 5, 8
Find the third proportion to the following :
3 and 15
What quantity must be added to each term of the ratio a + b: a - b to make it equal to (a + b)2 : (a - b)2 ?
If `a/b = c/d = r/f`, prove that `((a^2b^2 + c^2d^2 + e^2f^2)/(ab^3 + cd^3 + ef^3))^(3/2) = sqrt((ace)/(bdf)`
Verify the following:
39 : 65 : : 141 : 235
If a, b, c are in continued proportion, prove that: `(a + b)/(b + c) = (a^2(b - c))/(b^2(a - b)`.
What number must be added to each of the numbers 15, 17, 34 and 38 to make them proportional?
The shadow of a 3 m long stick is 4 m long. At the same time of the day, if the shadow of a flagstaff is 24 m long, how tall is the flagstaff?
Write True (T) or False (F) against the following statement:
8 : 9 : : 24 : 27
