Question

Please solve this question :-
(a+b√3)² = 4+7√3

Answer 1

Hey there!

( a + b√3 )² = 4 + 7√3

Applying square root on both sides,

a + b √3 = √ ( 4 + 7 √3 )

Now, We will find square root of 4 + 7√3

So,
Let

√ ( 4 + 7√3 ) = √x + √y

Now, Squaring on both sides

4 + 7√3 = x + y + 2√xy

So, x + y = 4 , xy = √49*3/4 =√147/4



Now,

( x - y) ² = (x + y )² - 4xy

x - y = √ ( 16 - √147 )

Now, x = 4 + √( 16 - √147 ) /2

x + y = 4

y = 4 - 2 - √(16 - √147)/2

y = 2 - √ ( 16 - √147 ) / 2

So,

a + b √3 = √ 4 + √ (16 - 7√3 ) / 2 + √ 2 - √( 16 - 7√3 )/2

The answer will be so complex.

So, I feel there might be errors in the question.


Let's consider your question to be :

a + b √3 = 4 + 7√3

We get values as a = 4 , b = 7 .

Answer 2

Hope this will help you ☺☺