Question

3√2x²-5x-√2=0 please answer the question​

Answer 1

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{x = \frac{6 - 5 \sqrt{2} }{7} }}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

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

$</p><p>\tt: \implies3 \sqrt{2 {x}^{2} } - 5x - \sqrt{2} = 0$

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

$\tt: \implies \: the \: solution \: of \: this$

Given Question

$</p><p>\tt: \implies3 \sqrt{2 {x}^{2} } - 5x - \sqrt{2} = 0$

$</p><p>\tt: \implies3 \sqrt{2} \times |x| - 5x - \sqrt{2} = 0$

$</p><p>\tt: \implies 3 \sqrt{2} - 5x - \sqrt{2} = 0 \: \: \: \: \: \: \: x \geqslant 0$

$</p><p>\tt: \implies3 \sqrt{2} \times ( - x) - 5x - \sqrt{2} = 0 \: \: \: \: \: \: x < 0$

$</p><p>\tt: \implies x = - \frac{6 + 5 \sqrt{2} }{7} = x \geqslant 0$

$</p><p>\tt: \implies 3 \sqrt{2} \times ( - x) - 5x - \sqrt{2} = 0 \: \: \: \: x < 0$

$</p><p>\tt: \implies 3 \sqrt{2} - 5x - \sqrt{2} = 0 \: \: \: \: \: \: \: x \geqslant 0$

$</p><p>\tt: \implies3 \sqrt{2} \times ( - x) - 5x - \sqrt{2} = 0 \: \: \: \: \: \: x < 0$

$</p><p>\tt: \implies x = - \frac{6 + 5 \sqrt{2} }{7} = x \geqslant 0$

$</p><p>\tt: \implies x = \frac{6 - 5 \sqrt{2} }{7} = x < 0$

$\tt: \implies x \: £ \: \cancel{0}$

$</p><p>\tt: \implies x = \frac{6 - 5 \sqrt{2} }{7} = x < 0$

$</p><p>\tt: \implies x = - \frac{6 + 5 \sqrt{2} }{7} = x \geqslant 0$

$</p><p>\tt: \implies x = \frac{6 - 5 \sqrt{2} }{7} = x < 0$

$\tt: \implies x \: £ \: \cancel{0}$

$</p><p>\tt: \implies x = \frac{6 - 5 \sqrt{2} }{7}$

$\green{\tt{\therefore{x = \frac{6 - 5 \sqrt{2} }{7} }}}$

Answer 2

$\huge \purple {Answer}$

3√2x²-5x-√2=0

By splitting middle term:-

3√2x²-6x + x-√2=0

3√2x(x-√2) + 1(x-√2)=0

(3√2x+1)(x-√2)=0

We got two equations from here:-

3√2x+1=0 and x-√2=0

For equation 3√2+1=0

3√2x=-1

x= $\frac {-1}{3√2}$

For equation x-√2=0

x=√2

Therefore, we have two solutions for this equation and solutions are x= $\frac {-1}{3√2}$ and x=√2.