simplify (5+2√3/7+4√3)
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( 5 + 2√3 ) / ( 7 + 4√3 )
= ( 5 + 2√3 ) / ( 7 + 4√3 ) × ( 7 – 4√3 ) / ( 7 – 4√3 )
= ( 5 + 2√3 ) ( 7 – 4√3 ) / [ ( 7)² – ( 4√3)² ]
= [ 5 ( 7 – 4√3 ) + 2√3 ( 7 – 4√3 ) ] / ( 49 – 48 )
= ( 35 – 20√3 + 14√3 – 24 ) / 1
= 11 – 6√3
( 5 + 2√3 ) / ( 7 + 4√3 )
= ( 5 + 2√3 ) / ( 7 + 4√3 ) × ( 7 – 4√3 ) / ( 7 – 4√3 )
= ( 5 + 2√3 ) ( 7 – 4√3 ) / [ ( 7)² – ( 4√3)² ]
= [ 5 ( 7 – 4√3 ) + 2√3 ( 7 – 4√3 ) ] / ( 49 – 48 )
= ( 35 – 20√3 + 14√3 – 24 ) / 1
= 11 – 6√3
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2
Answer:
Step-by-step explanation:
Given that:-
What to do:-
To rationalise the denominator
Solution:-
We have,
The denominator is 5+2√3. Multiplying the numerator and denominator by 7-4√3,
we get,
⬤ Applying Algebraic Identity
(a+b)(a-b) = a² - b² to the denominator
We get,
Hence the denominator is rationalised.
- I hope it's help with...☺
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