Question

If a+2b+3c=5 2ab+6bc+3ac=6thenthe value of [a power 2+4b power 2 +9cpower2 is 1 10 13 25

Answer 1

Answer:

13

Step-by-step explanation:

put a= 0, b= 1 , c =1

then, 0+2*1+3*1=5 , 2*0*1+6*1*1+3*0*1=6

then, a²+(4b)²+9c²= 0+4+9 = 13

Answer 2

∴a²+4b²+9c²=13

Step-by-step explanation:

Given,

a+2b+3c=5                   and 2ab +6bc+3ac=6

                                          ⇒2( 2ab +6bc+3ac)= 2×6

                                          ⇒4ab+12bc+6ac =12

Then

(a+2b+3c) =5

⇒(a+2b+3c)² =5²       [ squaring both sides]

⇒a²+4b²+9c²+2.a.2b+2.2b.3c+2.a.3c=25

⇒ a²+4b²+9c²+4ab+12bc+6ac=25

⇒a²+4b²+9c²+12=25               [∵4ab+12bc+6ac =12]

⇒a²+4b²+9c²=25-12

⇒a²+4b²+9c²=13