Question
Show that $(a - b)^2, (a^2 + b^2)$ and $(a + b)^2$^ are in A.P?
✓
Answer
$(a - b)^2, (a^2 + b^2)$ and $(a + b)^2$ are in A.P.
If $2(a^2 + b^2) = (a - b)^2 + (a + b)^2$
If $2(a^2 + b^2) = a^2 + b^2 - 2ab + a^2 + b^2 + 2ab$
If $2(a^2 + b^2) = 2a^2 + 2b^2 = 2(a^2 + b^2)$
Which is true
Hence proved.
If $2(a^2 + b^2) = (a - b)^2 + (a + b)^2$
If $2(a^2 + b^2) = a^2 + b^2 - 2ab + a^2 + b^2 + 2ab$
If $2(a^2 + b^2) = 2a^2 + 2b^2 = 2(a^2 + b^2)$
Which is true
Hence proved.
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