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MAVERICK [17]
2 years ago
7

NEED ANSWER ASAP -50 POINTS

Mathematics
1 answer:
lesantik [10]2 years ago
3 0

x+\dfrac{3}{x}=7

This is a disguised quadratic equation. To solve it, we must first multiply each term by <em>x</em> to get rid of the fraction:

x\times x+\dfrac{3}{x} \times x=7 \times x

x^2+3=7x

Now, we could solve this equation like a normal quadratic. Move all terms to the left side of the equation:

x^2-7x+3=0

To solve for <em>x</em>, we could use the quadratic formula:

x=\dfrac{-b \pm \sqrt{b^2-4ac}}{2a} where the given equation is ax^2+bx+c=0

Given x^2-7x+3=0, we know that:

a = 1

b = -7

c = 3

Plug in a, b and c:

x=\dfrac{-(-7) \pm \sqrt{(-7)^2-4(1)(3)}}{2(1)}\\\\x=\dfrac{7 \pm \sqrt{49-12}}{2}\\\\x=\dfrac{7 \pm \sqrt{37}}{2}

Therefore, the two solutions for x are x=\dfrac{7 - \sqrt{37}}{2} and x=\dfrac{7 + \sqrt{37}}{2}.

I hope this helps!

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