Question
If a(a + b + c) = 45, b(a + b + c) = 75 and c(a + b + c) = 105, then what is the value of (a^2 + b^2 + c^2)
यदि a (a + b + c) = 45, b (a + b + c) = 75 और c (a + b + c) = 105 है, तो (a^2 + b^2 + c^2) का मान क्या है?
Answer B.
B.a (a + b + c) = 45 …….(1)
b (a + b + c) = 75 ……..(2)
c (a + b + c)= 105 …….(3)
Add equation (i), (ii) and (iii),
(a + b + c) (a + b + c) =45 + 75 + 105
(a + b + c)^2 = 225
(a + b + c) = 15
Put the value of (a + b + c) in equation (1), (2) and (3).
a × 15 = 45
a=3
b × 15 = 75
b=5
c × 15 = 105
c=7
Now-
(a^2 + b^2 + c^2)=3^2+5^2+7^2
=9 + 25 + 49
=83
So the correct answer is option B.
B.a (a + b + c) = 45 …….(1)
b (a + b + c) = 75 ……..(2)
c (a + b + c)= 105 …….(3)
समीकरण (i), (ii) और (iii) को जोड़ने पर
(a + b + c) (a + b + c) =45 + 75 + 105
(a + b + c)^2 = 225
(a + b + c) = 15
(a + b + c)का मान समीकरण (1), (2) और (3) में रखने पर
a × 15 = 45
a=3
b × 15 = 75
b=5
c × 15 = 105
c=7
अब -
(a^2 + b^2 + c^2)=3^2+5^2+7^2
=9 + 25 + 49
=83
इसलिए सही उत्तर विकल्प B है।
