Question 55

If $$a + b - c = 12  and  a^2 + b^2 + c^2 = 110$$, then which among the following relations is true ?
(p) ab + bc + ca = 34,
(q) ab + bc - ca = 17,
(r) ab - bc + ca = 17,
(s) ab - bc - ca = 17

Solution

$$(a+b-c)^{2}=a^{2}+b^{2}+c^{2}+2ab-2bc-2ac$$

$$12^{2}=110+2(ab-bc-ac)$$

$$ab-bc-ca=17$$


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