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S_A_V [24]
3 years ago
15

Select whether the equation has a solution or not.

Mathematics
1 answer:
vredina [299]3 years ago
4 0

Answer: The equation has a solution .

Step-by-step explanation:

Since we have given that

\sqrt{x+1}=7-2\sqrt{x}

Squaring on both the sides, we get that,

x+1=(7-2\sqrt{x})^2\\\\x+1=49+4x-28\sqrt{x}\\\\3x+48-28\sqrt{x}=0

Let \sqrt{x}=y\implies x=y^2

So, our equation becomes,

3y^2-28y+48=0\\\\y=\dfrac{14}{3}\pm \dfrac{2\sqrt{13}}{3}\\\\\sqrt{x}=\dfrac{14}{3}\pm \dfrac{2\sqrt{13}}{3}\\\\x=(\dfrac{14}{3}\pm \dfrac{2\sqrt{13}}{3})^2

So, x=\dfrac{248}{9}\pm \dfrac{56\sqrt{13}}{9}

Hence, the equation has a solution .

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