Question

1. Write the roots of the equation 3(x-3)2 = 75.​

Answer 1

Answer:

3x-9*2=75

6x-18=75

6X=75+18

X=93/6

Answer 2

Answer:

$\displaystyle{\boxed{\red{\sf\:x\:=\:3\:\pm\:\sqrt{15}\:}}}$

Step-by-step-explanation:

The given quadratic equation is

3 ( x - 3 )² = 75

We have to find the roots of the equation.

Now,

3 ( x - 3 )² = 75

We know that,

( a - b )² = a² - 2ab + b²

⇒ 3 ( x² - 2 * x * 3 + 3² ) = 75

⇒ x² - 6x + 9 = 75 ÷ 3

⇒ x² - 6x + 9 = 15

⇒ x² - 6x + 9 - 15 = 0

⇒ x² - 6x - 6 = 0

Comparing with ax² + bx + c = 0, we get,

• a = 1
• b = - 6
• c = - 6

By quadratic formula,

$\displaystyle{\boxed{\pink{\sf\:x\:=\:\dfrac{-\:b\:\pm\:\sqrt{b^2\:-\:4ac}}{2a}\:}}}$

$\displaystyle{\implies\sf\:x\:=\:\dfrac{-\:(\:-\:6\:)\:\pm\:\sqrt{(\:-\:6\:)^2\:-\:4\:\times\:1\:\times\:(\:-\:6\:)}}{2\:\times\:1}}$

$\displaystyle{\implies\sf\:x\:=\:\dfrac{6\:\pm\:\sqrt{36\:+\:24}}{2}}$

$\displaystyle{\implies\sf\:x\:=\:\dfrac{6\:\pm\:\sqrt{60}}{2}}$

$\displaystyle{\implies\sf\:x\:=\:\dfrac{6\:\pm\:\sqrt{4\:\times\:15}}{2}}$

$\displaystyle{\implies\sf\:x\:=\:\dfrac{6\:\pm\:2\:\sqrt{15}}{2}}$

$\displaystyle{\implies\sf\:x\:=\:\dfrac{\cancel{2}\:(\:3\:\pm\:\sqrt{15}\:)}{\cancel{2}}}$

$\displaystyle{\implies\:\underline{\boxed{\red{\sf\:x\:=\:3\:\pm\:\sqrt{15}\:}}}}$

∴ The roots of the given quadratic equation are

$\displaystyle{\boxed{\red{\sf\:x\:=\:3\:+\:\sqrt{15}}}\:\quad\sf\&}$

$\displaystyle{\boxed{\red{\sf\:x\:=\:3\:-\:\sqrt{15}}}}$