Algebra Word Problems Solved | Algebra Help & Examples

High School
Algebra

Suppose $x^{1}$ and $x^{2}$ are solutions to $x^{2} + x + k = 0$ , if $x_{{1}}^{2} + x_{1} x_{2} + x_{2}^{2} = 2 k^{2}$ , find the value of k.

swtda03u7bo 2022-03-31

Suppose $x_{1}, x_{2}$ are roots of the equation $x = 5 - x^{2}$ . Find the equation with roots $\frac{1}{{(x_{1} + 1)}^{3}} and \frac{1}{{(x_{2} + 1)}^{3}}$ .
1) $125 x^{2} + 16 x = 1$
2) $125 x^{2} = 16 x + 1$
3) $125 x^{2} = 12 x + 1$
4) $125 x^{2} + 12 x = 1$

navantegipowh 2022-03-31

I have a quadratic equation, $b x^{2} + 2 a x + b = 0$ , with $a > b > 0$ . I can solve this as followings,
$x_{+} = \frac{- a + \sqrt{a^{2} - b^{2}}}{b}, x_{-} = \frac{- a - \sqrt{a^{2} - b^{2}}}{b},$
In my text book, an inequality equation, $x_{{+}}^{2} < 1 < x_{{-}}^{2}$ , is written with the solution, but I cannot derive the equation. If you can, please teach me the derivation.

Nadia Clayton 2022-03-31

I have a question where it is asking to find the values of a for which the graph of $f (x) = x^{2} + 2 x + a$ will intersect with its inverse. I solved it to the point where $a = - x (x - 3)$ , but how do you solve for a?

Sage Fry 2022-03-31

Solving the quadratic equation $a X^{2} + a Y^{2} + 2 b X + 2 c Y + d = 0$

Milton Robertson 2022-03-31

Solving the following equation:
$2^{x} + \log_{10} x - 2 = 0$

Dominique Pace 2022-03-31

Solving $x^{2} - ⌊ x ⌋ - 4 = 0$

navantegipowh 2022-03-31

I am having a difficult time understanding what I am doing wrong with quadratics.
$5 x^{2} - 15 x - 4 = 0$

Pizzadililehz 2022-03-31

Solving $2 + \frac{1}{\cos^{2} x} + \frac{5}{\cos x} = 0$

talpajocotefnf3 2022-03-31

How to think while solving question like this? If $a x^{2} + b x + c = 0$ has roots A and $A^{n}$ , then ${(a c^{n})}^{\frac{1}{n + 1}} + {(a^{n} c)}^{\frac{1}{n + 1}} + b = 0$

dotzis16xd 2022-03-31

Solving $\frac{x^{2} + 12 x + 4}{x + 2} = 6 \sqrt{x}$

svrstanojpkqx 2022-03-31

Solving $1 + x^{10 + {\log x}^{10 + {\log x}^{10 + \dots}}} = \frac{1}{\log x}$
To solve this equation I used $t = 1 + x^{10 + {\log x}^{10 + {\log x}^{10 + \dots}}}$ . LHS is equal to,
$1 + t = 1 + x^{10 + \log t}$
$t = x^{10 + \log t}$
$\log t = (\log x) \times (10 + \log t)$
$x = e^{\frac{\log t}{10 + \log t}}$
Hence the equation is equivalent to
$t + 1 = \frac{10 + \log t}{\log t}$
$t \log t = 10$
I'm not sure if this helps in solving the equation.

ICESSRAIPCELOtblt 2022-03-31

How to solve this quadratic equation (with x represented by a fraction containing a square root)?
If $x - \frac{4}{5} = \pm \frac{\sqrt{31}}{5}$ , how can I find the values of a and b in the following equation?
$5 x^{2} + a x + b = 0 ?$
I've tried substituting $(\frac{4}{5} \pm \frac{\sqrt{31}}{5})$ for x and got totally confused there.

aanvarendbq28 2022-03-31

Solving for y, given
$x = \frac{- 1 + \sqrt{1 + (4 \frac{y}{50})}}{2}$

diartrosiwk8o 2022-03-31

$2 a^{2} - b c - 9 a + 10 = 0$ then the range of ‘a' is?
Let a, b and c be real numbers such that $2 a^{2} - b c - 9 a + 10 = 0$ and $4 b^{2} + c^{2} + b c - 7 a - 8 = 0$ , then the range of ‘a' is?

Oxinailelpels3t14 2022-03-31

$9 B + C = A$ , $B = ?$

smaakt4ucq 2022-03-31

$2 x + 2 y = 174 x - y = 25$ What is the X - value of the solution to the system of equations

Caerswso1pc 2022-03-31

Solving for x in a (modified) quadratic
${(\sqrt{49 + 20 \sqrt{6}})}^{\sqrt{a \sqrt{a \sqrt{a \dots \infty}}}} + {(5 - 2 \sqrt{6})}^{x^{2} + x - 3 - \sqrt{x \sqrt{x \sqrt{x} \dots \infty}}} = 10$
where $where a = x^{2} - 3, (a \neq 0), Solve for x$

nastupnat0hh 2022-03-31

How to solve equation system with 3 parameters
$y = 2 x^{2} - 1$
$z = 2 y^{2} - 1$
$x = 2 z^{2} - 1$

Alexis Alexander 2022-03-31

$\log_{5} {- 3} = \frac{\log (3) + π i}{\log (5)}$ ?

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Algebra Word Problem Solutions