Question

solve by formula method
1) √2x²+7x+5√2=0​

Answer 1

Answer:

$\sqrt[]{2} x^{2} + 7x + \sqrt{2} =0$

we will use middle term splitting method.

split the middle term into two parts in such a way that the sum and product of those parts is 7 and $5\sqrt{2} X \sqrt{2} = 10$ respectively. These parts will be 5 and 2.

      $\sqrt{2}x^{2} +5x+2x+5\sqrt{2} =0\\x[\sqrt{2}x + 5]+\sqrt{2} [\sqrt{2}x+5]=0\\(x+\sqrt{2} )(\sqrt{2} x +5)=0\\Either x+\sqrt{2} =0 or \sqrt{2} x+5=0\\i.e. x=-\sqrt{2} , \frac{-5}{\sqrt{2} } \\i.e. x=i\sqrt{2}, \frac{-5\sqrt{2} }{2}$

where i=iota