Question

what is the value of a if 5+2√3/7+4√3=a-6√3​

Answer 1

Answer:

The answer is -

a = $\frac{35 + 72\sqrt{3}}{7}$

Step-by-step explanation:

Yo find the value of a, if 5 + 2√3/7 + 4√3 = a - 6√3​

Follow the basic rules of addition and subtraction [Chapter - NUMBER SYSTEM]

5 + $\frac{2\sqrt{3}}{7}$ + 4√3 = a - 6√3​

5 +  $\frac{2\sqrt{3}}{7}$ + 4√3 + 6√3​ = a [Using the rules of linear equation :- took - 6√3​ in the L.H.S]

Now take common

5 +  $\frac{2\sqrt{3}}{7}$ + √3​(4 + 6) = a

5 +  $\frac{2\sqrt{3}}{7}$ + 10√3​ = a

Now,

Take the L.C.M of the denominators 7 and 1

The L.C.M of 7 and 1 is 7

$\frac{2\sqrt{3}}{7}$ × $\frac{1}{1}$ and 10√3​ ×$\frac{7}{7}$ [To make the denominators equal]

$\frac{2\sqrt{3}}{7}$ and $\frac{70\sqrt{3}}{7}$

So,

5 +  $\frac{2\sqrt{3}}{7}$ + 10√3​ = a

5 + $\frac{2\sqrt{3}}{7}$ + $\frac{70\sqrt{3}}{7}$ = a

Now again take common

5 + $\frac{\sqrt{3}(2 + 70)}{7}$ = a

$\frac{5}{1}$ + $\frac{72\sqrt{3}}{7}$ = a

Now again take L.C.M of the denominators 1 and 7

The L.C.M 1 and 7 is 7

$\frac{5}{1}$ × $\frac{7}{7}$ and $\frac{72\sqrt{3}}{7}$ × $\frac{1}{1}$ [To make the denominators equal]

$\frac{35}{7}$ and $\frac{72\sqrt{3}}{7}$

So,

a = $\frac{5}{1}$ + $\frac{72\sqrt{3}}{7}$

a = $\frac{35}{7}$ + $\frac{72\sqrt{3}}{7}$

a = $\frac{35 + 72\sqrt{3}}{7}$

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