If x + y = 7 and xy = 10, find x2 + y2.
29
Use the identity \(x^2 + y^2 = (x+y)^2 - 2xy\).
Substituting the given values, \(x^2 + y^2 = 7^2 - 2(10) = 49 - 20\).
This gives \(x^2 + y^2 = 29\).
Similar Questions
For what value of k does \(x^2 -(k+3)x + (k+2) = 0\) have equal roots?
Find k such that \(x^2 -2(k+1)x + (k^2+1)=0\) has distinct real roots.
If x + y + z = 0 and x2 + y2 + z2 = 2, find x4 + y4 + z4.
Let x + y = 5 and x2 + y2 = 13. Find x and y.
Important Questions from Quadratic Equations
- The number of all possible positive integral values of $\alpha$ for which the roots of the quadratic equation, $10x^2 - 27x + \alpha = 0$ are rational numbers is:
The sum of all real values of x satisfying the equation
\(\rm (x^2 - 5x + 5) ^{x^2 + 4x - 60 }= 1\) is:
The number of integral values of $m$ for which the quadratic expression, $(10m-9)x^2 - 2mx + 1$, where $x \in \mathbb{R}$, is always positive, is
For a quadratic equation, ax 2+ bx + c = 0, if b 2– 4ac = 0, then the roots are,
If x + y + z = 0, then what is the value of \(\frac {x} {(yz)^2}+ \frac {y} {(xz)^2} + \frac {z} {(xy)^2}\)?
