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If a + b = 12, ab = 22, then (a2 + b2) is equal to?
Answer & Solution
Correct Answer:
Option
D
$$\eqalign{
& a + b = 12\,.....{\text{(i)}} \cr
& ab = 22\,.....{\text{(ii)}} \cr} $$
Squaring both sides of equation (i)
$$\eqalign{ & \Rightarrow {a^2} + {b^2} + 2ab = 144 \cr & \Rightarrow {a^2} + {b^2} + 2 \times 22 = 144 \cr & \Rightarrow {a^2} + {b^2} = 144 - 44 \cr & \Rightarrow {a^2} + {b^2} = 100 \cr} $$
Squaring both sides of equation (i)
$$\eqalign{ & \Rightarrow {a^2} + {b^2} + 2ab = 144 \cr & \Rightarrow {a^2} + {b^2} + 2 \times 22 = 144 \cr & \Rightarrow {a^2} + {b^2} = 144 - 44 \cr & \Rightarrow {a^2} + {b^2} = 100 \cr} $$
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