billy1123

05.12.2020 •

Mathematics

Triangle ABC is similar to triangle FGH. A12 B9 C15 G13.5 F18 Hx

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Ответ:

suewignall

25.01.2023

Mathematics

Option B is correct.

u= x+4

Step-by-step explanation:

Solve the equation:

(x+4)^2-3(x+4)-3 = 0

Using substitution:

Let u = x+4

then;

u^2-3u-3=0 ....[1]

For a quadratic equation ax^2+bx+c = 0 ....[2], then the solution is given by:

$x = \frac{-b \pm \sqrt{b^2-4ac}}{2a}$

On comparing equation [1] and [2] we have;

a = 1 , b = -3 and c = -3

then;

$u= \frac{-(-3) \pm \sqrt{(-3)^2-4(1)(-3)}}{2(1)}$

⇒ $u= \frac{3 \pm \sqrt{9+12}}{2}$

⇒ $u= \frac{3 \pm \sqrt{21}}{2}$

Substitute u = x+4

then;

⇒ $x+4= \frac{3 \pm \sqrt{21}}{2}$

Subtract 4 from both sides we have;

$x= \frac{3 \pm \sqrt{21}}{2} - 4= \frac{3 \pm \sqrt{21}-8}{2}$

⇒ $x= \frac{3 + \sqrt{21}-8}{2}= \frac{-5 + \sqrt{21}}{2}$

and

$x= \frac{3 - \sqrt{21}-8}{2}$

⇒ $x= \frac{-5 - \sqrt{21}}{2}$

Therefore, the solution for the given equation are,

$x= \frac{-5 - \sqrt{21}}{2}$ , $\frac{-5 + \sqrt{21}}{2}$

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