Is $(x-2)^2+1=2x-3$ a quadratic equation, then find the roots

Find the nature of roots of the quadratic equation:

$x^2+16x+64=0$

Examine the nature of the roots of the following quadratic equation:

$3x^2+8x+4=0$

Solve $x^2+5x+6$

If (a + b + c) = 17, and (a² + b² + c²) = 101, find the value of (a - b)² + (b - c)² + (c - a)².

If $(4y-\frac{4}{y})=11$ , find the value of $(y^2+\frac{1}{y^2})$.

If $x-\frac{1}{x} = 3$, then the value of $x^3-\frac{1}{x^3}$ is

f (a + b + c) = 12, and (a² + b² + c²) = 50, find the value of (a³ + b³ + c³ - 3abc)

If, $(x+\frac{1}{x})=4$, then the value of $x^4+\frac{1}{x^4}$ is:

If x + y = 4, then the value of (x³ + y³ + 12xy) is

If $x^4+\frac{1}{x^4}=34$, then the value of $(x-\frac{1}{x})^2$ will be

If a is positive and $a^2+\frac{1}{a^2}=7$, thenfind $a^3+\frac{1}{a^3}$.

If a = 299, b = 298, c = 297 then the value of 2a³ + 2b³ + 2c³ – 6abc is:

If a = 0.125 then what is value of $\sqrt{4a^2-4a+1}+3a$ ?

The value of \$\frac{6.35 \times 6.35 \times 6.35 + 3.65 \times 3.65 \times 3.65}{63.5 \times 63.5 + 36.5 \times 36.5 - 63.5 \times 36.5}$ is equal to

If x + y + z = 19, xyz = 216 and xy + yz + zx = 114, then the value of $\sqrt{x^3+y^3+z^3+xyz}$ is.

The value of $\frac{5.35\times{5.35}\times{5.35}+3.65\times{3.65}\times{3.65}}{53.5\times{53.5}+36.5\times{36.5}-53.5\times{36.5}}$ is:

If $\sqrt{11-3\sqrt{8}}=a+b\sqrt{2}$, then what is the value of (2a+3b)?

If (10a³ + 4b³) : (11a³ - 15b³) = 7 : 5, then (3a + 5b) : (9a - 2b) =?

If 27(x + y)³ - 8(x - y)³ = (x + 5y)(Ax² + By² + Cxy), then what is the value of (A + B - C)?

If a + b + c = 6, a³ + b³ + c³ - 3 abc = 342, and a² + b² + c² = 50, then what is the value of ab + bc + ca?

If a and b are two positive real numbers such that a + b = 20 and ab = 4, then the value of a³ + b³ is:

If a = 355, b = 356, c = 357, then find the value of a³ + b³ + c³ - 3abc.

If a + b = 10 and $\frac{3}{7}$ of ab = 9, then the value of a³ + b³ is:

If xy = 16 and x² + y² = 32, then the value of (x + y) is:

Find the factors of the expression 3x² – 5x – 8.

If $x^4+\frac{1}{x^4}=\frac{257}{16}$ then find $\frac{8}{13}(x^3+\frac{1}{x^3})$, where x>0.

If a + b = 8 and a + a² b + b + ab² = 128 then the positive value of a³ + b³ is:

If $x^2+\frac{1}{x^2}=38$ , then what is the value of $\left| {x - \frac{1}{x}} \right|$

If 2x + y = 6 and xy = 4, then find the value of 8x³ + y³ is:

If a - b = 4 and a³ - b³ = 88, then find the value of a² - b².

If x + y + z = 10, $x^3 + y^3 + z^3 = 75$ and xyz = 15, then find the value of $x^2 + y^2 + z^2-xy-yz-zx$

If $x =\sqrt{3} - 1$ and $y =\sqrt{3}+1$ then $\frac{(x^4-y^4)}{(x+y)^2}$ is equal to ?

$A=\frac{x-1}{x+1}$, then the value of $A-\frac{1}{A}$ is:

If $a^3 + b^3 + c^3 - 3abc = 126,$ a + b + c = 6, then the value of (ab + bc + ca) is:

If $a+b=\frac{7}{3}$ and $a^2+b^2=\frac{31}{9},$ find$27(a^3+b^3)$

In the expansion of $(2x + y )^3-(2x - y)^3$, the coefficient of $x^2y$ is:

If a + b + c = 6, $a^2 + b^2 + c^2 = 30$ and $a^3 + b^3 + c^3 = 165,$ then the value of 4abc is:

If a + b + c = 7 and $a^3 + b^3 + c^3-3abc = 175$, then what is the value of (ab + bc + ca)?

If $4a+\frac{1}{5a}=4$ , then the value of $25a^2+\frac{1}{16a^2}$ is:

If $x+\frac{1}{2x}=3$, find the value of $8x^3+\frac{1}{x^3}$.

If $2(a^2 + b^2) = (a + b)^2$ then,