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Alexxx [7]
3 years ago
10

If 5 + 2 root 3 / 7 + 4 root 3 = a - b root 3, find a and b.​

Mathematics
2 answers:
xxMikexx [17]3 years ago
7 0

Answer:

a = 11, b = 6

Step-by-step explanation:

Given

\frac{5+2\sqrt{3} }{7+4\sqrt{3} }

Rationalise the denominator by multiplying numerator/ denominator by the conjugate of the denominator.

The conjugate of 7 + 4\sqrt{3} is 7 - 4\sqrt{3}

= \frac{(5+2\sqrt{3})(7-4\sqrt{3})  }{(7+4\sqrt{3})(7-4\sqrt{3}  } ← expand numerator/ denominator using FOIL

= \frac{35-20\sqrt{3}+14\sqrt{3}-24  }{49-28\sqrt{3}+28\sqrt{3}-48  }

= \frac{11-6\sqrt{3} }{1}

= 11 - 6\sqrt{3}

with a = 11 and b = 6

Serggg [28]3 years ago
4 0

Answer:

lhs = (5+2√3)/(7+4√3)

= [(5+2√3)(7-4√3)]/[(7-4√3)(7+4√3)]

=[35-20√3+14√3-24]/[7²-(4√3)²]

=[11-6√3]/[49-48]

=11-6√3

therefore

11-6√3 = a+b√3

compare both sides

a= 11, b= -6

Step-by-step explanation:

Hope this answer helps you :)

Have a great day

Mark brainliest

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