Math Olympiad Exponential Equation | Math Olympiad Questions | Find the Value of x

[@chemingerful]

Good and quite trivial solution

[@benachourmohsen4806]

Very nice

[@ajitandyokothakur7191]

Your solution is simple and elegant; the two in the comments are not. Dr. Ajit Thakur (USA).

[@ali777ff9]

You. Are. Crazy. &. Also. Making. Studens. Crazy.

[@kareolaussen819]

x=1 is an obvious solution; x=-1 requires some more work to find.

[@richardbailey2001]

Why was this video header written in English, when it should have been written in some language completely different.

[@BADMOSH_chhora-2701]

thumbnail dekhke 5 min mein solve kar diya😂

[@BlackBoard114]

Good

[@ManojkantSamal]

^=read as to the power
*=reas as square root
As per question
(8^x+27^x)/(12^x+18^x)=7/6
Let's explain LHS
N=8^X+27^X
={(2^3)^x}+{(3^3)^x}
={(2^x)^3}+{(3^x)^3}
Let 2^x=R, 3^x=A
So,
R^3+A^3
=(R+A)^3- 3RA(R+A)
=(R+A){(R+A)^2-3RA}
=(R+A){R^2+A^2+2RA-3RA}
=(R+A){R^2+A^2-RA}
Now explain D
12^X+18^X
=6^X(2^X+3^X)
=(2^X×3^X)(2^X+3^X)
=RA(R+A)
N/D=(R+A){R^2+A^2-RA}/RA(R+A)
=(R^2+A^2-RA)/RA
=(R^2/RA)+(A^2/RA)-(RA/RA)
=(R/A)+(A/R)-1
=[(R/A)+{1/(R/A)}-1
Let (R/A)=T
So,
{T+1/T)}-1
{(T^2+1)/T}-1
Now
{(T^2+1)/T}-1=7/6
(T^2+1)/T = (7/6)+1=(7+6)/6
So,
(T2+1)/T = 13/6
6T^2+6=13T
6T2-13T+6=0
6T^2-9T-4T+6=0
3T(2T-3)-2(2T-3)0
(2T-3)(3T-2)=0
So,
2T-3=0 or 3T-2=0
2T=3 or 3T=2
T=3/2 or T=2/3
(R/A)=(3/2) or (R/A)=(2/3)
Case 1
(R/A)=(3/2)
{(2^x)/(3^x)}=(3/2)
(2/3)^x=(3/2)
(2/3)^x=1/(2/3)
(2/3)^x=(2/3)^(-1)
X=(-1)
Case 2
(2/3)^x= (2/3)
(2/3)^x=(2/3)^1
X=1
Hence
X=1or (-1)

[@SanatGhosh-03m]

6a^2 - 13ab +6b^2 middle factor hoga na kaya

[@dardoburgos3179]

X= 1.

[@НеллиПшено]

Решаем методом устного счета.
8+27=35
12+18=30
35/30=7/6
x=1
Good luck!

[@allenporter6586]

x=1, (8+27)/(12+18) = 35/30 = 7/6 duh

[@luisgonzalezgomez6014]

Wasn´t there a 6 in the final expression? you ignored it?, and I´m sorry for the stupid question.

[@carlorff1965]

Divide both sides by 6. And you ged rid of the 6.