Given that a^3+3 a b^2 b^2+3 a^2 b =63 62 . Using Componendo and … - Vidyadip

Question

Given that $\frac{a^3+3 a b^2}{b^2+3 a^2 b}=\frac{63}{62}$.
Using Componendo and Dividendo find $a : b.$

✓

Answer

We have
$\frac{a^3+3 a b^2}{b^2+3 a^2 b}=\frac{63}{62}$
App. compoenedo and dividendo
$\frac{a^3+3 a b^2+b^3+3 a^2 b}{a^3+3 a b^2-b^3-3 a^2 b}=\frac{63+62}{63-62} $
$ \frac{a^3+3 a b^2+b^3+3 a^2 b}{a^3+3 a b^2-b^3-3 a^2 b}=\frac{125}{1}$
$ \frac{(a+b)^3}{(a-b)^3}=\frac{125}{1} $
$ \frac{a+b}{a-b}=\frac{5}{1}$
Again Applying Componendo & Dividendo
$\frac{a+b+a-b}{a+b-a+b}=\frac{5+1}{5-1} $
$ \frac{2 a}{2 b}=\frac{6}{4}$
$ a : b =3: 2$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "[3 marks sum]" from Ratio and Proportion→Ratio and Proportion — all question types→Mathematics STD 10 question papers→ICSE Board STD 10 question papers→ICSE Board question paper generator→

Similar questions

The internal and external diameters of a hollow hemi$-$spherical vessel are $21 \ cm$ and $28 \ cm$ respectively. Find volume of material of the vessel.

Find the rnedian of the first $15$ whole numbers .

Solve for x : 1 + 4 + 7 + 10 + … + x = 287.

Find the 16th term of the A.P. $7,11,15,19$ $\qquad$ Also find the sum of the first 6 terms.

Calculate the percentage income in the following investment:
Rs 7,168 paying 15% when a Rs 80 share is available at 40% premium.

Solve the equation $9 x^2+\frac{3 x}{4}+2=0$ if possible for real values of $x$

David opened a Recurring Deposit Account in a bank and deposited Rs 300 per month for two years. If he received Rs 7,725 at the time of maturity, find the rate of interest per annum.

The heights of 60 students of a class are given in the following table :

Height(in cm)	150-155	155-158	158-160	160-165	165-172
No. of students	8	20	25	4	3

Find the probability that the height of a student lies in the interval
(i) 155-158

A card is drawn from a well shuffled pack of 52 cards. Find the probability that the card drawn is: a red or a king

If one root of the equation $2x^2– px + 4 = 0$ is $2,$ find the other root. Also find the value of $p.$