Grade 8Algebra
If √3+√5=a/√(b-√c), what is the value of (a+b+c) for a,b, c real and c is square free number.
If √3+√5=a/√(b-√c), what is the value of (a+b+c) for a,b, c real and c is square free number.
1 Answer
Vikas TU
Approved Tutor Answer10 Years ago√3+√5=a/√(b-√c)
squaring both sides,
3 + 5 + 2√15 = a^2/(b-√c)
8 + 2√15 = a^2/(b-√c)
Rationalize the RHS side,
.i.e. a^2/(b-√c) = > a^2*(b+√c)/(b^2-c)
it can be further written as:
a^2*b/(b^2-c) + a^2*√c/(b^2-c)
Hence,
final eqn.
8 + 2√15 = a^2*b/(b^2-c) + a^2*√c/(b^2-c)
Now comparing rational and irrational numbers ogether we get,
a^2*b/(b^2-c) = 8 …........................(1)
and
a^2*√c/(b^2-c) = 2√15
Therfore,
c = 15
and a^2/(b^2-c) = 2
Therfore, from eqn. (1)
b = 4
and
a = √2 or -√2
add themnow.
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