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प्रश्न
In the following, determine whether the given values are solutions of the given equation or not:
`x^2-sqrt2x-4=0`, `x=-sqrt2`, `x=-2sqrt2`
उत्तर
We have been given that,
`x^2-sqrt2x-4=0`, `x=-sqrt2`, `x=-2sqrt2`
Now if `x=-sqrt2` is a solution of the equation then it should satisfy the equation.
So, substituting `x=-sqrt2` in the equation, we get
`x^2-sqrt2x-4`
`=(-sqrt2)^2-sqrt2(-sqrt2)-4`
= 2 + 2 - 4
= 0
Hence `x=-sqrt2` is a solution of the quadratic equation.
Also, if `x=-2sqrt2` is a solution of the equation then it should satisfy the equation.
So, substituting `x=-2sqrt2` in the equation, we get
`x^2-sqrt2x-4`
`(-2sqrt2)^2-sqrt2(-2sqrt2)-4`
= 8 + 4 - 4
= 8
Hence `x=-2sqrt2`is not a solution of the quadratic equation.
Therefore, from the above results we find out that `x=-sqrt2` is a solution but `x=-2sqrt2`is not a solution of the given quadratic equation.
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