Question

Root 2 x square -3x -2 root 2 =0

Answer 1

Answer:

$\huge{\boxed{\sf{ Roots\:of\:this\:eqn=2\sqrt{2}\:and\frac{-1}{\sqrt{2}} }}}$

Step-by-step explanation:

$\huge{\boxed{\sf{ SOLUTION- }}}$

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

$\huge{\boxed{\sf{ METHOD(1) }}}$

$\huge{\boxed{\sf{ middle\:term\:spliting }}}$

$\sqrt{2} {x}^{2} - 3x - 2 \sqrt{2} = 0 \\ \sqrt{2} {x}^{2} - 4x + x - 2 \sqrt{2} = 0 \\ \sqrt{2} x(x - 2 \sqrt{2} ) +1 (x - 2 \sqrt{2} ) = 0 \\ ( \sqrt{2}x + 1)(x - 2 \sqrt{2} ) = 0 \\ \sqrt{2}x + 1 = 0 \\ \sqrt{2} x = - 1 \\ x = \frac{ - 1}{ \sqrt{2} }----1st\:root \\ x - 2 \sqrt{2} = 0 \\ x = 2 \sqrt{2}----2nd\:root$

$\huge{\boxed{\sf{ METHOD(2)}}}$

$\huge{\boxed{\sf{ QUADRATIC\:FORMULA}}}$

$d = {b}^{2} - 4ac \\ \: \: \: \: = ({ - 3})^{2} - (4 \times \sqrt{2} \times 2\sqrt{2} ) \\ \: \: \: \: = 9 + 16 \\ \: \: \: \: = 25 \\ x = \frac{ - b + \sqrt{d} }{2a} \\ x = \frac{3 + 5}{2 \sqrt{2} } \\ x = \frac{8}{2 \sqrt{2} } \\ x = \frac{4 \sqrt{2} }{2} \\ x = 2 \sqrt{2} - - - - 1st \: root \\ x = \frac{ - b - \sqrt{d} }{2a} \\ x = \frac{3 - 5}{2 \sqrt{2} } \\ x = \frac{ - 2}{2 \sqrt{2} } \\ x = \frac{ - 1}{ \sqrt{2} } - - - - 2nd \: root$

$\huge{\boxed{\sf{\green{ Roots\:of\:this\:eqn=2\sqrt{2}\:and\frac{-1}{\sqrt{2}} }}}}$

Answer 2

Answer:

√2x^-3x-2√2=0

Step-by-step explanation:

√2x^-3x-2√2=0

√2x^-4x+x-2√2=0

√2x(x-2√2)+1(x-2√2)=0

(√2x+1)(x-2√2)=0

√2x+1=0

√2x=-1

x=-1/√2

x=2√2