Advertisements
Advertisements
Question
If p, q and r in continued proportion, then prove the following:
(p + q + r )(p - q + r) = p2 + q2 + r2
Advertisements
Solution
p : q :: q : r ⇒ q2 = pr
(p + q + r )(p - q + r) = p2 + q2 + r2
LHS
(p + q + r)(p - q + r)
= p2 + pq + pr - pq - q2 - qr + pr + qr + r2
= p2 + 2pr - q2 + r2
= p2 + 2q2 - q2 + r2
= p2 + q2 + r2 = RHS
LHS = RHS. Hence, proved.
APPEARS IN
RELATED QUESTIONS
If a, b, c and d are in proportion prove that `sqrt((4a^2 + 9b^2)/(4c^2 + 9d^2)) = ((xa^3 - 4yb^3)/(xc^3 - 5yd^3))^(1/3)`
If q is the mean proportional between p and r prove that `(p^3 + q^3 + r^3)/(p^2q^2r^2) = 1/p^3 + 1/q^3 = 1/r^3`
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 b is the mean proportional between a and c, prove that `(a^2 - b^2 + c^2)/(a^-2 -b^-2 + c^-2)` = b4.
If a, b, c, d are in continued proportion, prove that:
`sqrt(ab) - sqrt(bc) + sqrt(cd) = sqrt((a - b + c) (b - c + d)`
If 9, x, x 49 are in proportion, find the value of x.
A gets double of what B gets and B gets double of what C gets. Find A : B and B : C and verify whether the result is in proportion or not
Write True (T) or False (F) against the following statement:
12 : 18 : : 28 : 12
Are the following statements true?
99 kg : 45 kg = ₹ 44 : ₹ 20
If a, b, c and d are in proportion, the value of `(8a^2 - 5b^2)/(8c^2 - 5d^2)` is equal to ______.
