Question

Under root 6x^2-4x-2under root 6=0

Answer 1

Answer:

Given

√( x + 1) = 4

We raise both sides to power 2 in order to clear the square root.

[ √( x + 1) ] 2 = 4 2

and simplify

x + 1 = 16

Solve for x.

x = 15

NOTE: Since we squared both sides without putting any conditions, extraneous solutions may be introduced, checking the solutions is necessary.

Left side (LS) of the given equation when x = 15

LS = √(x + 1) = √(15 + 1) = 4

Right Side (RS) of the given equation when x = 15

RS = 4

Answer 2

correct question➡

$\large\ \sqrt{6} {x}^{2} - 4x - 2 \sqrt{6} = 0$

TO FIND➡value of 'x'

using formula ➡

$\bf\red{\underline{split \: the \: middle \: term \: method}}$

$\bf\ \implies: \sqrt{6} {x}^{2} - 4x - 2 \sqrt{6} = 0 \\ \\ \bigstar \bigstar \: 2 \sqrt{6} \times \sqrt{6} = 2 \times 6 = 12 \\ \\ \bigstar \bigstar \: 12 = \underline{2 \times 3} \times \underline{2} \\ \\ \bf\boxed{ \mapsto:6x \times 2x = 12 {x}^{2} \: \: and \: 6x - 2x = 4x} \\ \\ \bf\ \implies: \sqrt{6} {x}^{2} - (6x - 2x) - 2 \sqrt{6} = 0 \\ \\ \bf\ \implies: \sqrt{6}{x}^{2} - 6x + 2x - 2 \sqrt{6} = 0 \\ \\ \bf\ \implies: \sqrt{6} x(x - \sqrt{6} ) + 2(x - \sqrt{6} ) = 0 \\ \\ \bf\boxed{ \implies:(x - \sqrt{6} )( \sqrt{6}x + 2) = 0} \\ \\ \huge\ \: now \\ \\ \bf\pink {\implies:x - \sqrt{6} = 0} \: \: \: \: \: \: \: or \: \: \: \: \: \bf\green{ \implies: \sqrt{6}x + 2 = 0 } \\ \\ \bf\pink{ \boxed{ \implies:x = \sqrt{6}} } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \bf\green{ \boxed{ \implies:x = \frac{ - 2}{ \sqrt{6} } }} \\ \\ \\ \large\boxed{ \fcolorbox{red}{purple}{hope \: it \: help \: you}}$