Question

76. Solve for x, √2x+ 9+x=3.​

Answer 1

Step-by-step explanation:

√2x+9+x=3

√2x+x=-6

x(√2+1)=-6

x=-6/√2+1

Answer 2

Given that,

$\sf{ \sqrt{2}x + 9 + x = 3 }$

To find the value of x.

Now,

$\sf{ \sqrt{2}x + 9 + x = 3 } \\ \\ \implies \: \sf{ \sqrt{2}x + x = - 6 } \\ \\ \implies \: \sf{x( \sqrt{2} + 1) = - 6} \\ \\ \implies \: \sf{x = \frac{ - 6}{ \sqrt{2} + 1 } }$

Rationalising the denominator,

But why do we rationalize here,it is because there should be no radical signs in the denominator of a fraction.

So,

$\sf{x = \frac{ - 6}{ \sqrt{2} + 1} } \\ \\ \sf{ \: \: \: \: = \frac{ - 6}{ \sqrt{2} + 1} \times \frac{ \sqrt{2} - 1}{ \sqrt{2} - 1 } } \\ \\ \sf{ \: \: \: \: = \frac{ - 6( \sqrt{2} - 1) }{ \sqrt{2 {}^{2} } - 1 {}^{2} } } \\ \\ \sf{ \: \: = - 6 \sqrt{2} + 6 }$

The value of x is -6√2+6