Question

Split the middle term of x^2+2 root 2x -6

Answer 1

Given

a equation

x²+2√2x-6

To find

spilt the middile term

x²+2√2x-6

Solution

Factorise it

we have to spilt 2√2x in such a way that the sum become 2√2x and product be -6

x²+2√2x-6

=>x²+3√2x-√2x-6

=>x(x+3√2)-√2(x+3√2)

=>(x-√2) (x+3√2)

Hence,the middle term break into (3√2x-√2x). To satisfy the need to break I n factor

Answer 2

$\huge {\red {\mathfrak{Question :-}}}$

• Split the middle term of $x^2+2 \sqrt{2x} - 6$.

$\huge {\pink{\mathfrak{Solution :-}}}$

$\underline {\bold{Given:}}$

• $x^2+2 \sqrt{2x} - 6$.

$\underline {\bold{To\:Find}}$

• Split the middle term of $x^2+2 \sqrt{2x} - 6$.

We have to find a number whose sum = $\bf{2 \sqrt{2x}}$ and product =-6.

$\implies {x}^{2} + 2 \sqrt{2x} - 6 \\ \\ \implies {x}^{2} + 3 \sqrt{2x} - \sqrt{2x} - 6 \\ \\ \implies x(x + 3 \sqrt{2} ) - \sqrt{2} (x+3 \sqrt{2} ) \\ \\ \implies (x + 3 \sqrt{2} )( x - \sqrt{2})$

$\green{\therefore {\tt{The\: answer\: is\:(x + 3 \sqrt{2} )( x - \sqrt{2}).}}}$

$\rule{307}{2}$