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.
Aenakshee Roy , 9 Years ago
Grade 8
Algebra> If √3+√5=a/√(b-√c), what is the value of ...
1 AnswersVikas TU
√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.
Approved Last Activity: 9 Years ago
LIVE ONLINE CLASSES
Prepraring for the competition made easy just by live online class.
Full Live Access
Study Material
Live Doubts Solving
Daily Class Assignments
Other Related Questions on algebra
Can we divide two vectors? If this is possible then how?
Can we divide two vectors? If this is possible then how?
algebra
1 Answer Available
Last Activity: 2 Years ago
How do you write “the product of 18 and q” as an algebraic expression?
How do you write “the product of 18 and q” as an algebraic expression?
algebra
1 Answer Available
Last Activity: 2 Years ago
दहावीच्या आय सी एस इ विद्यार्थ्यांनी पुढे काय करायला पाहिजे
दहावीच्या आय सी एस इ विद्यार्थ्यांनी पुढे काय करायला पाहिजे
algebra
1 Answer Available
Last Activity: 3 Years ago