Question

x²-(1+√2)x + √2 = 0. chapter name quadratic equations​

Answer 1

Answer:

x= {1,√2}

Step-by-step explanation:

You can solve it in 2 ways:

1. Middle term split method.
2. Using quadratic formula.

I'll be doing it with 1st method here,

x²-(1+√2)x + √2 = 0

Can be written as:

x²-x-√2x + √2 = 0

Solvinf furthur,

x(x-1) -√2(x-1) =0

(x-√2)(x-1) =1

Therefore,

x= 1 and x= √2

Answer 2

x=1 and √2

Step-by-step explanation:

To solve:-

$\sf x^2-(1+\sqrt{2})x+\sqrt{2}=0$

Used method:-

Mid-term splitation

Solution:-

$\tt \twoheadrightarrow \: {x}^{2} - (1 + \sqrt{2} )x + \sqrt{2} = 0 \\ \\ \tt \twoheadrightarrow \: {x}^{2} - x - \sqrt{2} x + \sqrt{2} = 0 \\ \\ \tt \twoheadrightarrow \: x(x - 1) - \sqrt{2} (x - 1) = 0 \\ \\ \tt \twoheadrightarrow \: (x - 1)( x - \sqrt{2} ) = 0 \\ \\ \tt \twoheadrightarrow \: (x - 1) = 0 \: or \: (x - \sqrt{2} ) = 0 \\ \\ \tt \twoheadrightarrow \: x = 1 \: or \: x = \sqrt{2}$