A system of three linear equations in three variables is inconsistent if their planes

\(\frac { x }{ { x }^{ 2 }-25 } -\frac { 8 }{ { x }^{ 2 }+6x+5 } \) gives

The square root of \(\frac { 256{ x }^{ 8 }{ y }^{ 4 }{ z }^{ 10 } }{ 25{ x }^{ 6 }{ y }^{ 6 }{ z }^{ 6 } } \) is equal to

If the roots of the equation q²x² + p²x + r² = 0 are the squares of the roots of the equation qx² + px + r = 0, then q, p, r are in __________.

Solve \(\frac { x }{ 2 } -1=\frac { y }{ 6 } +1=\frac { z }{ 7 } +2\); \(\frac { y }{ 3 } +\frac { z }{ 2 } =13\)

The sum of thrice the first number, second number and twice the third number is 5. If thrice the second number is subtracted from the sum of first number and thrice the third we get 2. If the third number is subtracted from the sum of twice the first, thrice the second, we get 1. Find the numbers.

Solve the following system of linear equations in three variables.
x + y + z = 6; 2x + 3y + 4z = 20;
3x + 2y + 5z = 22

Using quadratic formula solve the following equations.9x²-9(a+b)x+(2a²+5ab+2b²)=0

Prove that the equation x²(a²+b²)+2x(ac+bd)+(c²+ d²) = 0 has no real root if ad≠bc.

Write down the quadratic equation in general form for which sum and product of the roots are given below.
9, 14

Draw the graph of y = x² + 4x + 3 and hence find the roots of x² + x + 1 = 0

The sum of two numbers is 15. If the sum of their reciprocals is \(\frac{3}{10}\), find the numbers.

A chess board contains 64 equal squares and the area of each square is 6.25 cm², A border round the board is 2 cm wide.

Find the GCD of the following by division algorithm 2x⁴ + 13x³ + 27x²+23x + 7, x³ + 3x² + 3x + 1, x² + 2x + 1

If –4 is a root of the equation x² + px - 4 = 0 and if the equation x² + px + q has equal roots, find the values of p and q.