Question

a+b/√ab=6 find the ratio of a and b

Answer 1

your answer is a:b==>
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Answer 2

Answer:

Either 17 - 12√2 or 17 + 12√2

Step-by-step explanation:

Given :

( a + b ) / ( √ab ) = 6

==> a / √ab + b / √ab = 6

==> √( a² / ab ) + √ ( b² / ab ) = 6

==> √a / √b + √b / √a = 6

Take √a / √b as x

==> x + 1 / x = 6

==> ( x² + 1 ) / x = 6

==> x² + 1 = 6 x

==> x² + 6 x + 1 = 0

Use : x = [ - b ± √ ( b² - 4 ac ) ] / 2 a

==> x = [ -6 ± √ ( 6² - 4.1.1 ) ] / 2

==> x = [ - 6 ± √ (36 - 4 ) ] / 2

==> x = [ - 6 ± √32 ] / 2

==> x = [ - 6 ± 4√2 ] / 2

==> x = 2 [ - 3 ± 2√2 ] / 2

==> x = ± 2√2 - 3

Hence either :

x = 2√2 - 3

or :

x = -2√2 - 3

Now :

√a / √b = x

==> (√a / √b) = x²

==> a / b = x²

Either :

a / b = ( 2√2 - 3 )²

==> a / b = 8 - 12√2 + 9

==> a / b = 17 - 12√2

or :

a / b = ( - 2√2 - 3 )²

==> a / b = 8 + 9 + 12√2

==> a / b =  17 + 12√2

Hope it helps !

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