Find the fourth proportional to: x^3 - y^2, x^4 + x^2y^2+ y^4, x … - Vidyadip

Question

Find the fourth proportional to:
$x^3 - y^2, x^4 + x^2y^2+ y^4, x - y$.

✓

Answer

Let A be the fourth proportional then
$ x ^3- y ^2: x ^4+ x ^2 y ^2+ y ^4= x - y : A $
$\Rightarrow \frac{x^3-y^3}{x^4+x^2 y^2+y^4}=\frac{x-y}{ A } $
$ \Rightarrow A \left( x ^3- y ^3\right)=( x - y )\left( x ^4+ x ^2 y ^2+ y ^4\right) $
$\Rightarrow A =\frac{(x-y)\left(x^4+x^2 y^2+y^4\right)}{x^3-y^3} $
$ \Rightarrow A =\frac{(x-y)\left(x^2+y^2+x y\right)\left(x^2+y^2-x y\right)}{(x-y)\left(x^2+x y+y^2\right)} $
$\Rightarrow A = x ^2+ y ^2- xy .$

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

Simplify: $\frac{\sin A}{\cot A+\operatorname{cosec} A}-\frac{\sin A}{\cot A-\operatorname{cosec} A}$

Points $(3,0)$ and $(-1,0)$ are invarient points under reflection in the line $L_1 ;$ point $(0,-3)$ and $(0,1)$ are invarient points on reflection in line $L _2$.
(i) Write the equation of the line $L_1$ and $L_2$.
(ii) Write down the images of points $P (3,4)$ and $Q (-5,-2)$ on reflection in $L _1$. Name the images as $P ^{\prime}$ and $Q ^{\prime}$ respectively.
(iii) Write down the images of P and Q on reflection in $L _2$. Name the image as $P ^{\prime \prime}$ and $Q ^{\prime \prime}$ respectively.

Find the triplicate ratio of the following:
$\sqrt{15}: \sqrt{18}$

Draw histogram for the following data:

Class-interval	0 - 10	10 - 20	20 - 30	30 - 40	40 - 50	50 - 60
Frequency	12	20	26	18	10	6

Mr. Sonu has a recurring deposit account and deposits ₹ $ 750$ per month for 2 years. If he gets ₹ $ 19,125$ at the time of maturity, find the rate of interest.

Find the distance of a point $(13 , -9)$ from another point on the line $y = 0$ whose abscissa is $1.$

Which term of the A.P. $105, 101, 97 …$ is the first negative term?

Which term of the A.P. 3, 10, 17,… will be 84 more than its 13th term?

If $\frac{a}{b}=\frac{c}{d}=\frac{e}{f}$, prove that$(a b+c d+e f)^2=\left(a^2+c^2+e^2\right)\left(b^2+d^2+f^2\right)$.

If $sinA + cosA = m$ and $secA + cosecA = n$, prove that $n(m^2 - 1) = 2m$