Advertisements
Advertisements
Question
If a, b, care in continued proportion, then show that `(a + b)^2/(ab) = (b + c)^2/(bc)`.
Since a, b, c are in continued proportion
∴ `a/b = square/square` = k(say)
⇒ b = `square`, a = `square` = `square`.k = `square`.k2
Now, L.H.S. = `(a + b)^2/(a.square) = (square + square)^2/(square*square)`
= `(squarek^2(k + 1)^2)/(square*square)`
= `(k + 1)^2/square`
R.H.S. = `(b + c)^2/(b.square) = (square + square)^2/(square*square) = (square (k + 1)^2)/(square*square)`
= `(k + 1)^2/square`
L.H.S. = `square`
Solution
Since a, b, c are in continued proportion
∴ `a/b = bb b/bbc` = k(say)
⇒ b = ck, a = bk = ck.k = c.k2
Now, L.H.S. = `(a + b)^2/(a.bb b) = (bb(ck^2) + bb(ck))^2/(bb(ck^2)*bb(ck))`
= `(bb(c^2)k^2(k + 1)^2)/(bb(c^2)*bb(k^3))`
= `(k + 1)^2/bbk`
R.H.S. = `(b + c)^2/(b.bbc) = (bb(ck) + bbc)^2/(bb(ck)*bbc) = (bb(c^2) (k + 1)^2)/(bb(c^2)*bbk)`
= `(k + 1)^2/bbk`
L.H.S. = R.H.S
Hence proved
APPEARS IN
RELATED QUESTIONS
Find the roots of the following quadratic equations, if they exist, by the method of completing the square `4x^2 + 4sqrt3x + 3 = 0`
Find the roots of the following quadratic equations, if they exist, by the method of completing the square 2x2 + x + 4 = 0
Find the roots of the quadratic equations 2x2 + x – 4 = 0 by applying the quadratic formula.
Find the roots of the quadratic equations 2x2 + x + 4 = 0 by applying the quadratic formula.
Two water taps together can fill a tank in `9 3/8`hours. The tap of larger diameter takes 10 hours less than the smaller one to fill the tank separately. Find the time in which each tap can separately fill the tank.
Sum of the areas of two squares is 468 m2. If the difference of their perimeters is 24 m, find the sides of the two squares.
Find the roots of the following quadratic equations (if they exist) by the method of completing the square.
`x^2-4sqrt2x+6=0`
Find the roots of the following quadratic equations (if they exist) by the method of completing the square.
`x^2-(sqrt2+1)x+sqrt2=0`
`x^2-(sqrt2+1)x+sqrt2=0`
The area of right -angled triangle is 165 sq meters. Determine its base and altitude if the latter exceeds the former by 7 meters.
Solve the following quadratic equation by completing the square method.
9y2 – 12y + 2 = 0
Solve the following quadratic equation by completing the square method.
m2 – 5m = –3
Fill in the gaps and complete.
If α, β are roots of quadratic equation,
Find the value of discriminant.
2y2 – 5y + 10 = 0
Sum of the area of two squares is 400 cm2. If the difference of their perimeters is 16 cm, find the sides of two squares.
To fill a swimming pool two pipes are used. If the pipe of larger diameter used for 4 hours and the pipe of smaller diameter for 9 hours, only half of the pool can be filled. Find, how long it would take for each pipe to fill the pool separately, if the pipe of smaller diameter takes 10 hours more than the pipe of larger diameter to fill the pool?
In a flight of 600 km, an aircraft was slowed due to bad weather. Its average speed for the trip was reduced by 200 km/hr and the time of the flight increased by 30 minutes. Find the scheduled duration of the flight.
Rohini had scored 10 more marks in her mathematics test out of 30 marks, 9 times these marks would have been the square of her actual marks. How many marks did she get on the test?
Find the value of x, if `(4/7)^x (7/4)^(2x) = 343/64`.
