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 `x/a = y/b = z/c` prove that `(2x^3 - 3y^3 + 4z^3)/(2a^3 - 3b^3 + 4c^3) = ((2x - 3y + 4z)/(2a - 3b + 4c))^3`
Check whether the following numbers are in continued proportion.
2, 4, 8
If y is the mean proportional between x and y; show that y(x+z) is the mean p roporti ona I between x2+ y2 and y2+ z2
Find the value of x in the following proportions : 2.5 : 1.5 = x : 3
If x + 5 is the mean proportion between x + 2 and x + 9, find the value of x.
In covering 111 km, a car consumes 6 L of petrol. How many kilometers will it go to 10 L of petrol?
If a, b, c and d are in proportion, prove that: `abcd [(1/a^2 + 1/b^2 + 1/c^2 + 1/d^2]` = a2 + b2 + c2 + d2
If a, b, c are in continued proportion, prove that: `(1)/a^3 + (1)/b^3 + (1)/c^3 = a/(b^2c^2) + b/(c^2a^2) + c/(a^2b^2)`
If two ratios are equal, then they are in ______.
A recipe calls for 1 cup of milk for every `2 1/2` cups of flour to make a cake that would feed 6 persons. How many cups of both flour and milk will be needed to make a similar cake for 8 people?
