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Question

If $$a + b + c = 10$$ and $$a^2\, +\, b^2\, +\, c^2\, =\, 36$$, then $$ab + bc + ca =$$ .......... .



A
136
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B
64
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C
32
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D
68
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Solution

The correct option is C $$32$$

$$a + b + c = 10$$

Squaring on both sides, we get

$$a^2\, +\, b^2\, +\, c^2\, +\, 2ab\, +\, 2bc\, +\, 2ca\, =\, 100$$

$$36\, +\, 2(ab\, +\, bc\, +\, ca)\, =\, 100$$

$$2(ab\, +\, bc\, +\, ca)\, =\, 100\, -\, 36\, =\, 64$$

$$ab\, +\, bc\, +\, ca\, =\, \displaystyle \frac{64}{2}\, =\, 32$$


Mathematics

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