Question

67. If 1+ m + n=15, Im+mn + nl = 85, find the value of 12 + m2 + n2.
(A) 66
(B) 60
(C) 55
(D) 45​

Answer 1

Given :

• l + m + n=15

• Im+mn + nl = 85

To find :

• l²+m²+n²

Solution :

We know that :-

$\sf {(a + b + c)}^{2} = {a}^{2} + {b}^{2} + {c}^{2} + 2(ab + bc + ca)$

Therefore :-

$\sf \implies {(l + m + n)}^{2} = {l}^{2} + {m}^{2} + {n}^{2} + 2(lm + mn + ln)$

Now it's given that :-l + m + n=15 and Im+mn + nl = 85

$\sf \implies {(15)}^{2} = {l}^{2} + {m}^{2} + {n}^{2} + (2 \times 85)$

we know that :- 15²= 225

$\sf \implies225= {l}^{2} + {m}^{2} + {n}^{2} + 170$

$\sf \implies225 - 170= {l}^{2} + {m}^{2} + {n}^{2}$

$\sf \implies55= {l}^{2} + {m}^{2} + {n}^{2}$

Therefore the value of l²+m²+n² = 55

Answer :

Option (c) 55 is correct answer.