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Solve your equation using trail and improvement. A number plus ten times its square root is is equal to one thousand

Sagot :

MrRoyal

Answer:

[tex]x \approx 729[/tex]

Step-by-step explanation:

Given

Let the number be x

So:

[tex]x + 10\sqrt x = 1000[/tex]

Required

Using trial and improvement, find x

This implies that we keep guessing the values of x until we get a value that match the equation.

Let

[tex]x = 625[/tex]

So, we have:

[tex]x + 10\sqrt x = 1000[/tex]

[tex]625 + 10 *\sqrt{625}[/tex]

Take the square root of 625

[tex]625 + 10 *\sqrt{625} = 625 + 10 *25[/tex]

[tex]625 + 10 *\sqrt{625} = 625 + 250[/tex]

[tex]625 + 10 *\sqrt{625} = 875[/tex]

Let

[tex]x = 729[/tex]

So, we have:

[tex]x + 10\sqrt x = 1000[/tex]

[tex]729 + 10 * \sqrt{729}[/tex]

Take the square root of 729

[tex]729 + 10 * \sqrt{729} = 729 + 10 * 27[/tex]

[tex]729 + 10 * \sqrt{729} = 729 + 270[/tex]

[tex]729 + 10 * \sqrt{729} = 999[/tex]

At this point, we can conclude that x is approximately 729 because

[tex]999 \approx 1000[/tex]

So:

[tex]x \approx 729[/tex]

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