3 years ago

Hello,i need help with this question:

Mathematics

1 answer:

Keith_Richards [23]3 years ago

5 0

Answer:

the value of x is 23

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A = √7 + √c and b = √63 + √d where c and d are positive integers.

mrs_skeptik [129]

Answer:

$\displaystyle a:b=\frac{1}{3}$

Step-by-step explanation:

<u>Ratios </u>

We are given the following relations:

$a=\sqrt{7}+\sqrt{c}\qquad \qquad[1]$

$b=\sqrt{63}+\sqrt{d}\qquad \qquad[2]$

$\displaystyle \frac{c}{d}=\frac{1}{9} \qquad \qquad [3]$

From [3]:

$9c=d$

Replacing into [2]:

$b=\sqrt{63}+\sqrt{9c}$

We can express 63=9*7:

$b=\sqrt{9*7}+\sqrt{9c}$

Taking the square root of 9:

$b=3\sqrt{7}+3\sqrt{c}$

Factoring:

$b=3(\sqrt{7}+\sqrt{c})$

Find the ration a:b:

$\displaystyle a:b=\frac{\sqrt{7}+\sqrt{c}}{3(\sqrt{7}+\sqrt{c})}$

Simplifying:

$\boxed{a:b=\frac{1}{3}}$

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Answer:

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Step-by-step explanation:

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