UPSC CAPF Assistant Commandant Model Paper 3

GIVEN:
a + b + c = 11
ab + bc + ca = 36
CONCEPT:
Algebra
FORMULA USED:
(a+b+c)2=a2+b2+c2+2‌ab+2‌bc+2‌ca
CALCULATION:
a + b + c = 11
ab + bc + ca = 36
We know that:
(a+b+c)2=a2+b2+c2+2‌ab+2‌bc+2‌ca
⇒a2+b2+c2=121−72
⇒a2+b2+c2=49
⇒a2+b2=49−c2
We know that sum of two squares are always greater than or equal to zero ‘0’.
a2+b2≥0
⇒49−c2≥0
⇒49≥c2
⇒c2≤49
⇒c≤7
∴ Maximum value which ‘c’ can take is 7.