Math, asked by hanumanrana24, 9 months ago

prove of a,b,c are in continued proportion
a2+b2 b(a+c)
-----------. = --------------
b(a+c). ​b2+c2​

Answers

Answered by manojatindia
8

Step-by-step explanation:

a, b and c are the continued proportion

a : b = b : c

⇒ a/b = b/c

⇒ b2 = ac

Now a/c = a2 + b2/b2 + c2

⇒ a(b2 + c2) = c(a2 + b2)

L.H.S. = a(b2 + c2) ⇒ a(ac + c2) ⇒ ac(a + c)

R.H.S. = c(a2 + b2) ⇒ c(a2 + ac) ⇒ ac(a + c)

L.H.S. = R.H.S. Hence proved.

Related questions

0

votes

1

answer

If x/a = y/b = z/c, prove that x3/a2 + y3/b2 + z3/c2 = (x + y + z)3/(a + b + c)2

asked Feb 23, 2019 in Class X Maths by priya12 (-12,637 points)

ratio and proportion

0

votes

1

answer

If a/b = c/d = e/f, prove that (ab + cd + ef)2 = (a2 + c2 + e2)(b2 + d2 + f2).

asked Feb 23, 2019 in Class X Maths by aditya23 (-2,155 points)

ratio and proportion

0

votes

1

answer

If b is the mean proportional between a and c, prove that a2 – b2 + c2/a-2 – b-2 + c-2 = b4.

asked Feb 22, 2019 in Class X Maths by aditya23 (-2,155 points)

ratio and proportion

0

votes

1

answer

If a, b, c, d are in continued proportion, prove that :

asked Feb 23, 2019 in Class X Maths by priya12 (-12,637 points)

ratio and proportion

0

votes

1

answer

If a, b, c, d are in continued proportion, prove that (b – c)2 + (c – a)2 + (d – b)2 = (d – a)2

asked Feb 23, 2019 in Class X Maths by navnit40 (-4,945 points)

ratio and proportion

0

votes

1

answer

If a : b = c : d, show that (a – c)b2 : (b – d)cd = (a2 – b2 – ab) : (c2 – d2 – cd)

asked Feb 23, 2019 in Class X Maths by aditya23 (-2,155 points)

ratio and proportion

0

votes

1

answer

If ax = by = cz, prove that x2/yz + y2/zx + z2/xy = bc/a2 + ca/b2 + ab/c2

asked Feb 22, 2019 in Class X Maths by priya12 (-12,637 points)

ratio and proportion

0

votes

1

answer

If a sin θ + b cos θ = c , then prove that a cos θ - b sin θ = the whole under root a2 + b2 - c2 .

asked Nov 10, 2017 in Class X Maths by akansha Expert (2.2k points)

+2

votes

1

answer

If a,b,c are all non-zero and a + b + c = 0, prove that a2/bc + b2/ca+ c2/ab = 3.

asked Sep 14, 2018 in Class IX Maths by aditya23 (-2,155 points)

polynomials

0

votes

1

answer

If a : b with a ≠ b is the duplicate ratio of a + c : b + c, show that c2 = ab.

Similar questions