Math, asked by mandurizvi7089, 6 months ago

If 3+√7/3-√7=2a+3b√7 find a and b

Answers

Answered by rohitkhajuria90
0

Answer:

a=4 and b=1

Steps

Given

 \frac{3 +  \sqrt{7} }{3 -  \sqrt{7} }  = 2a + 3b \sqrt{7}

To find a and b

Solve LHS

 \frac{3 +  \sqrt{7} }{3 -  \sqrt{7} } \\  multipy \: numerator   \: and \: denomintor \: by \: 3 +  \sqrt{7}  \\  = \frac{3 +  \sqrt{7} }{3 -  \sqrt{7} } \times \frac{3 +  \sqrt{7} }{3  +   \sqrt{7} } \\  =  \frac{9 + 3 \sqrt{7} + 3 \sqrt{7} + 7  }{ {3}^{2}  -  { (\sqrt{7}) }^{2}  }  \: ({{as \:  {a}^{2}  -  {b}^{2}  = ( + b)(a - b)}}) \\  \\  =  \frac{16 + 6 \sqrt{7}}{9 - 7}   \\  = \frac{16 + 6 \sqrt{7}}{2} \\  = 8 + 3 \sqrt{7}

Now,

2a + 3b \sqrt{7}  = 8 + 3 \sqrt{7} \\  2a + 3b \sqrt{7}  =( 2 \times 4) + (3 \times 1 )\sqrt{7}

Hence, a=4 and b=1

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