Question

X2+2root 2x-6 by splitting the middle term

Answer 1

↑ Here is your answer ↓
_____________________________________________________________
_____________________________________________________________

$x^2 + 2 \sqrt 2 x - 6 = 0$

{ Sum = $2 \sqrt 2$, Product = $-6$ }

  ∴ Required numbers are $3 \sqrt 2$ and $-\sqrt 2$

$x^2 + 3 \sqrt 2 x - \sqrt 2 x - 6 = 0$

$x(x + 3 \sqrt 2) - \sqrt 2 (x + 3 \sqrt 2)$

$(x - \sqrt 2)(x+ 3 \sqrt 2)$

Hence,

$x = \sqrt 2$

$x = - 3 \sqrt 2$

Answer 2

Hey friend, Harish here.

Here is your answer:

Given:

An expression x² + 2√2 x - 6.

To Do:

Factorize the above expression.

Solution:

$x^{2} +2 \sqrt{2}x - 6$

Here (a + b) = 2 √2  &  ab = -6.

Then,

a = -√2  & b = 3√2

⇒  $x^{2} - \sqrt{2}x +3 \sqrt{2}x - 6$

⇒  $x(x- \sqrt{2})+3 \sqrt{2}(x - \sqrt{2})$

⇒  $(x+3 \sqrt{2}) (x- \sqrt{2})$

Hence the expression is factorized using splitting the middle term.
____________________________________________________

Hope  my answer is helpful to you.