Question

middle term split x²-2√5x+3

Answer 1

Answer:

Step-by-step explanation:

Given : $x^2-2\sqrt{5}x+3$

To Find: middle term split

Solution:

$x^2-2\sqrt{5}x+3=0$

$x^2-(\sqrt{5}+\sqrt{2})x-(\sqrt{5}-\sqrt{2})x+3=0$

$x(x-(\sqrt{5}+\sqrt{2}))-(\sqrt{5}-\sqrt{2})(x-(\sqrt{5}+\sqrt{2}))=0$

$(x-(\sqrt{5}+\sqrt{2}))(x-(\sqrt{5}-\sqrt{2}))=0$

$x=(\sqrt{5}+\sqrt{2}) , x=(\sqrt{5}-\sqrt{2})=0$

Answer 2

Given:

$x^2-2\sqrt{5}x+3=0$

To Find:

Middle terms = ?

Solution:

In factorize the given equation, we get

⇒  $x^2-(\sqrt{5}+\sqrt{2})x-(\sqrt{5}-\sqrt{2})x+3=0$

On taking common, we get

⇒  $x[x-(\sqrt{5}+\sqrt{2})]-(\sqrt{5}-\sqrt{2})[x-(\sqrt{5}+\sqrt{2})]=0$

⇒  $[x-(\sqrt{5}+\sqrt{2})][x-(\sqrt{5}-\sqrt{2})]=0$

⇒  $x=(\sqrt{5}+\sqrt{2})$

Or,

⇒  $x=(\sqrt{5}-\sqrt{2} )$

So that the middle terms are "√5+√2" and "√5-√2".