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Arithmetic Mean and Range

Say true or f...

Question

Say true or false.
The A.M. between $(a - b)^{2}$ and $(a + b)^{2}$ is $a^{2} + b^{2}$ .

True

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False

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Solution

The correct option is A True
$(a - b)^{2} = a^{2} - 2 a b + b^{2}$
$(a + b)^{2} = a^{2} + 2 a b + b^{2}$
Adding the two, we get $(a - b)^{2} + (a + b)^{2} = 2 a^{2} + 2 b^{2}$
Dividing the whole equation by $2$ , we get, AM $=$ $a^{2} + b^{2}$

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Similar questions

A = [\begin{matrix} 2 & - 1 0 & 1 \end{matrix}]

B = [\begin{matrix} 1 & 0 - 1 & - 1 \end{matrix}],

(A + B)^{2} = A^{2} + A B + B A + B^{2} = A^{2} + 2 A B + B^{2}

A

B

A^{2} - B^{2} = (A - B) (A + B)

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

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

(b^{2} + c^{2} - a^{2}) tan A = (c^{2} + a^{2} - b^{2}) tan B

(a^{2} + b^{2} - c^{2}) tan C

A B = A

B A = B

A^{2} = A

B^{2} = B

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