Question

if a+b=7 and ab=6find a^2-b^2

Answer 1

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Answer 2

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Nice Question,Thanks
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given ab = 6 and

a + b = 7 _______eq.(1)

by squaring both side , we get

a^2 + b^2 + 2ab = 49

a^2 + b^2 = 49 - 2ab. ___eq.(2)

a^2 - b^2 =___________?

a^2 - b^2=( a + b ) ( a - b )

NOTE : (a - b)=√( a^2 + b^2 - 2ab )

a^2 - b^2=( a + b )√( a^2 + b^2 - 2ab )

a^2 - b^2=( a + b )√( 49 - 2ab - 2ab )

a^2 - b^2=(a + b )√(49 - 4ab ) ____eq(3)

now put given value of

ab = 6 , and( a + b ) = 7 in eq.(3),we get

a^2 - b^2=( 7 ) √(49 - 4(6) )

a^2 - b^2= 7 × √( 49 - 24 )

a^2 - b^2= 7 × √25

a^2 - b^2= 7 × 5 = 35

therefore , a^2 - b^2 = 35

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Your Answer: a^2 - b^2 = 35
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