Question

If 2a+3b+4c=10 and 6ab+12bc+8ac=32, then what is the value of 4a2+9b2+16c2?

Answer 1

Answer:

We know

(x+y+z)(x2+y2+z2−xy−yz−zx)=x3+y3+z3−3xyz

∴(2a+3b−4c)(4a2+9b2+16c2+12bc+8ca)

=(2a)3+(3b)3+(−4c)3−3×(2a)×(3b)×(−4c)

=8a3+27b3−64c3+72abc

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Answer 2

Answer:

the value of 4a2+9b2+16c2=36

Step-by-step explanation:

( 2a+3b+4c)^2=(10 )^2

4a2+9b2+16c2+12ab+24bc+16ac=100

4a2+9b2+16c3+2(6ab+12bc+8ac)=100

4a2+9b2+16c3+2(32)=100

4a2+9b2+16c3=100-64

4a2+9b2+16c3=36