Question

If 2a +3b =7 and ab=2,find 4a^2 + 9b^2

Answer 1

(2a +3b) =7

Square on both sides,

(2a+3b)² =7²

4a² +9b² + 2(6ab) =49

4a² +9b² +12ab =49

4a² +9b² +12(2)=49

4a² +9b² +24=49

4a² +9b² =49-24

4a² +9b² = 25

Answer 2

4a^2+9b^2
=(2a+3b)^2-2×2a×3b
=(7)^2-2×2×3×2
=49-24
=25

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