Question

If a+2b=9 and ab=7, find the value of a²+4b²

Answer 1

refer to the attachement

Answer 2

Answer

Step-by-step explanation:-

Given, ab = 7        --- : ( 1 )

         a + 2b = 9    ---: ( 2 )

To find : a^2 + 4b^2

          ⇒ a^2 + ( 2b )^2

If we observe, a^2 + ( 2b )^2 can be obtained if we applying the formula, ( x + y )^2 on a + 2b . So

Formula : ( x + y )^2 = x^2 + y^2 + 2xy

⇒ ( a + 2b ) = 9

Squaring on both sides : -

⇒ ( a + 2b )^ 2= 9^2

⇒ ( a )^2 + ( 2b )^2 + 2( a*2b ) = 81

⇒ a^2 + 4b^2 + 4ab = 81

⇒ a^2 + 4b^2 = 81 - 4ab

∴ a^2 + 4b^2 = 81 - 4ab

But in the question, value of ab is also given And that 7, so

a^2 + 4b^2 = 81 - 4( 7 )  

a^2 + 4b^2 = 81 - 28  

a^2 + 4b^2 = 53  

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