Farhan's problem of real numbers 2
Algebra
Level
pending
If the real numbers a,b,c satisfy a=2b+√2 and ab+√3c²/2+1/4=0, evaluate bc/a.
The answer is 0.
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1 solution
Substitute a=2b+√2 into ab+√3c²/2+1/4=0, then 2b²+√2b+(√3c²/2+1/4)=0. Since b is a real number, Discriminant of above equation=(√2)²-4x2x(√3c²/2+1/4)=-4√3c²>=0, that is c²<=0. On the other hand, c is a real number, thus c²>=0. As a conclusion, c=0. Therefore bc/a=0.