3 years ago

Which of the following is true?

Mathematics

1 answer:

butalik [34]3 years ago

3 0

Answer:

Step-by-step explanation:Its multiple choice next time just guess and keep trying

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If a = √3-√11 and b = 1 /a, then find a² - b²

Serga [27]

If $b=\frac1a$ , then by rationalizing the denominator we can rewrite

$b = \dfrac1{\sqrt3-\sqrt{11}} \times \dfrac{\sqrt3+\sqrt{11}}{\sqrt3+\sqrt{11}} = \dfrac{\sqrt3+\sqrt{11}}{\left(\sqrt3\right)^2-\left(\sqrt{11}\right)^2} = -\dfrac{\sqrt3+\sqrt{11}}8$

Now,

$a^2 - b^2 = (a-b) (a+b)$

and

$a - b = \sqrt3 - \sqrt{11} + \dfrac{\sqrt3 + \sqrt{11}}8 = \dfrac{9\sqrt3 - 7\sqrt{11}}8$

$a + b = \sqrt3 - \sqrt{11} - \dfrac{\sqrt3 + \sqrt{11}}8 = \dfrac{7\sqrt3 - 9\sqrt{11}}8$

$\implies a^2 - b^2 = \dfrac{\left(9\sqrt3 - 7\sqrt{11}\right) \left(7\sqrt3 - 9\sqrt{11}\right)}{64} = \boxed{\dfrac{441 - 65\sqrt{33}}{32}}$

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2 years ago

Slove the following system of equations <br> 7x+2y=-25<br> -5x-4y=5

Bingel [31]

Answer:

x=-5

y=5

Step-by-step explanation:

Explanation is in picture (Where the lines cross is your answer)

Tip: Try using desmo calculator. Where the lines cross is your answer so all you need to do is type in your equations

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3 years ago

The length of a rectangle field is 20 less than its width. The area of the field is 12000 ft ^2. What is the width of the field?

Naddik [55]

L = w - 20

12000 = w × ( w - 20 )
12000 = w^2 - 20w
w^2 - 20w - 12000 = 0
( w - 10 ) ( w - 10 ) = 0

width = 10

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Inga [223]

A picture is needed for this

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