Math Olympiad | A Nice Rational Equation | VIJAY Maths

[@pradyumnanayak9844]

👍

[@Bheeshma-l2g]

👍👍👍

[@Rocio62154]

EXCELLENTONIO!!

[@babupinjari5698]

Excellent

[@vijaymaths5483]

Thank you

[@srinivasch-re2oq]

Very simple
Take a common in numerator
And find all sums by taking LCM of all denominators
And find a,

[@PrithwirajSen-nj6qq]

We notice that .1/3*5
=1/2(1/3 -1/5)
Hence the expression in LHS
=a/2(1/3 -1/13)=a/2(10/39)=10a/78
Hence
10a =7800
a=780

[@PrithwirajSen-nj6qq]

Thank you, Sir

[@guyhoghton399]

Let *_S = 1/15 + 1/35 + 1/63 + 1/99 + 1/143_*
∴ _2S = (1/3 - 1/5) + (1/5 - 1/7) + (1/7 - 1/9) + (1/9 - 1/11) + (1/11 - 1/13)_
∴ _2S = 1/3 - 1/13 = 10/39_
⇒ _S = 5/39_
Equation is *_aS = 100_*
⇒ *_a = 100/S = (100 * 39) / 5 = 780_*

[@spottymaldoon]

Very nicely done!

[@guyhoghton399]

@@spottymaldoon Thank you.

[@wes9627]

(3*7*11*13+9*11*13+5*11*13+5*7*13+5*7*9)a=5*7*9*11*13*100; a=4504500/5775=780