<span>To predict f(x) when x equals 8 we simply substitute.
So f(x) = 25x2 28x + 585
f(8) = 25 (8)^2 - 28 (8) + 585
f(8) = 25 * 64 - 224 + 585
f(8) = 1600 - 224 + 585 = 1961
Hencse f(8) = 1961</span>
Answer:
![\huge\boxed{x+\dfrac{1}{x}=(13+2\sqrt{42})+(13-2\sqrt{42})=26}](https://tex.z-dn.net/?f=%5Chuge%5Cboxed%7Bx%2B%5Cdfrac%7B1%7D%7Bx%7D%3D%2813%2B2%5Csqrt%7B42%7D%29%2B%2813-2%5Csqrt%7B42%7D%29%3D26%7D)
Step-by-step explanation:
![x=\dfrac{\sqrt7+\sqrt6}{\sqrt7-\sqrt6}\cdot\dfrac{\sqrt7+\sqrt6}{\sqrt7+\sqrt6}=\dfrac{(\sqrt7+\sqrt6)^2}{(\sqrt7-\sqrt6)(\sqrt6+\sqrt7)}\\\\\\\text{use}\ (a+b)^2=a^2+2ab+b^2\ \text{and}\ (a-b)(a+b)=a^2-b^2](https://tex.z-dn.net/?f=x%3D%5Cdfrac%7B%5Csqrt7%2B%5Csqrt6%7D%7B%5Csqrt7-%5Csqrt6%7D%5Ccdot%5Cdfrac%7B%5Csqrt7%2B%5Csqrt6%7D%7B%5Csqrt7%2B%5Csqrt6%7D%3D%5Cdfrac%7B%28%5Csqrt7%2B%5Csqrt6%29%5E2%7D%7B%28%5Csqrt7-%5Csqrt6%29%28%5Csqrt6%2B%5Csqrt7%29%7D%5C%5C%5C%5C%5C%5C%5Ctext%7Buse%7D%5C%20%28a%2Bb%29%5E2%3Da%5E2%2B2ab%2Bb%5E2%5C%20%5Ctext%7Band%7D%5C%20%28a-b%29%28a%2Bb%29%3Da%5E2-b%5E2)
![x=\dfrac{(\sqrt7)^2+(2)(\sqrt7)(\sqrt6)+(\sqrt6)^2}{(\sqrt7)^2-(\sqrt6)^2}\\\\\\\text{use}\ (\sqrt{a})^2=a,\ \text{for}\ a\geq0\\\\\\x=\dfrac{7+2\sqrt{42}+6}{7-6}=\dfrac{13+2\sqrt{42}}{1}=13+2\sqrt{42}\\\\\dfrac{1}{x}=\dfrac{1}{13+2\sqrt{42}}\cdot\dfrac{13-2\sqrt{42}}{13-2\sqrt{42}}=\dfrac{13-2\sqrt{42}}{13^2-(2\sqrt{42})^2}=\dfrac{13-2\sqrt{42}}{169-168}\\\\\dfrac{1}{x}=13-2\sqrt{42}](https://tex.z-dn.net/?f=x%3D%5Cdfrac%7B%28%5Csqrt7%29%5E2%2B%282%29%28%5Csqrt7%29%28%5Csqrt6%29%2B%28%5Csqrt6%29%5E2%7D%7B%28%5Csqrt7%29%5E2-%28%5Csqrt6%29%5E2%7D%5C%5C%5C%5C%5C%5C%5Ctext%7Buse%7D%5C%20%28%5Csqrt%7Ba%7D%29%5E2%3Da%2C%5C%20%5Ctext%7Bfor%7D%5C%20a%5Cgeq0%5C%5C%5C%5C%5C%5Cx%3D%5Cdfrac%7B7%2B2%5Csqrt%7B42%7D%2B6%7D%7B7-6%7D%3D%5Cdfrac%7B13%2B2%5Csqrt%7B42%7D%7D%7B1%7D%3D13%2B2%5Csqrt%7B42%7D%5C%5C%5C%5C%5Cdfrac%7B1%7D%7Bx%7D%3D%5Cdfrac%7B1%7D%7B13%2B2%5Csqrt%7B42%7D%7D%5Ccdot%5Cdfrac%7B13-2%5Csqrt%7B42%7D%7D%7B13-2%5Csqrt%7B42%7D%7D%3D%5Cdfrac%7B13-2%5Csqrt%7B42%7D%7D%7B13%5E2-%282%5Csqrt%7B42%7D%29%5E2%7D%3D%5Cdfrac%7B13-2%5Csqrt%7B42%7D%7D%7B169-168%7D%5C%5C%5C%5C%5Cdfrac%7B1%7D%7Bx%7D%3D13-2%5Csqrt%7B42%7D)
Answer:
10x -18
Step-by-step explanation:
add the same things together
Answer:
3/16
Step-by-step explanation:
Easy!! USE A CALCULATOR! LOL!
Answer:
the simplest form is just the simplest a number can be, or least complicated, for example,
2^2 +2 -5 is a lot bigger than it needs to be, so if you simplify it to the simplest form by doing all these small equations, you would get, 1.