Advertisements
Advertisements
प्रश्न
If x2 + y2 = 29 and xy = 2, find the value of x - y.
Advertisements
उत्तर
We have:
\[\left( x - y \right)^2 = x^2 - 2xy + y^2 \]
\[ \Rightarrow \left( x - y \right) = \pm \sqrt{x^2 - 2xy + y^2}\]
\[ \Rightarrow \left( x + y \right) = \pm \sqrt{29 - 2 \times 2} (\because x^2 + y^2 = 29 \text { and } xy = 2)\]
\[ \Rightarrow \left( x + y \right) = \pm \sqrt{29 - 4}\]
\[ \Rightarrow \left( x + y \right) = \pm \sqrt{25}\]
\[ \Rightarrow \left( x + y \right) = \pm 5\]
संबंधित प्रश्न
If 3x + 5y = 11 and xy = 2, find the value of 9x2 + 25y2
Find the value of the following expression: 16x2 + 24x + 9, when \[x = \frac{7}{4}\]
Find the value of the following expression: 64x2 + 81y2 + 144xy, when x = 11 and \[y = \frac{4}{3}\]
Multiply: x2 + 4y2 + 2xy − 3x + 6y + 9 by x − 2y + 3
Divide: 35a3 + 3a2b - 2ab2 by 5a - b
Express the following as an algebraic expression:
The subtraction of 5m from 3n and then adding 9p to it.
The figure shows the dimensions of a wall having a window and a door of a room. Write an algebraic expression for the area of the wall to be painted.
Shiv works in a mall and gets paid ₹ 50 per hour. Last week he worked for 7 hours and this week he will work for x hours. Write an algebraic expression for the money paid to him for both the weeks.
A school has a rectangular playground with length x and breadth y and a square lawn with side x as shown in the figure given below. What is the total perimeter of both of them combined together?
The rate of planting the grass is ₹ x per square metre. Find the cost of planting the grass on a triangular lawn whose base is y metres and height is z metres.
