Show that (a - b)^2, (a^2 + b^2) and (a + b)^2 are in AP.... | VSA 2m | Maths | SuperPadhai

Arithmetic Progressions > Question

VSA2 marksYear: 2020MediumCBSE Class 10

arithmetic-progressionscommon-differenceproof

Question

Show that

(a - b)^{2}

,

(a^{2} + b^{2})

and

(a + b)^{2}

are in AP.

Solution

1

(a^{2} + b^{2}) - (a - b)^{2} = (a^{2} + b^{2}) - (a^{2} - 2 ab + b^{2}) = 2 ab

+1 mark

2

(a + b)^{2} - (a^{2} + b^{2}) = (a^{2} + 2 ab + b^{2}) - (a^{2} + b^{2}) = 2 ab

Common difference is same,

∴

given terms are in AP.

+1 mark

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