Question

Solve the simultaneous equation 2 exponent x+y equals 6 and 3 exponent x-y equals 4.

Answer 1

first equation:-
x^2 +y=6
from here we get,
x^2=6-y(by bringing y to r.h.s)
and ,
x=(6-y)^1/2
x=√6-y.........................1
 
in the 2nd equation
x^3-y =4
x^3=4+y
x=(4+y)^1/3........................................2

now equate 1 and 2
 
√6-y=(4+y)^1/3
(6-y)^1/2=(4+y)^1/3
(6-y)^3/2=4+y


(6-y)^3=(4+y)^2
(a-b)^3=a^3-b^3-3ab(a-b)
(a+b)^2=a^2+b^2+2ab

so,(6-y)^3=6^3-y^3-3*6*y(6-y)
=216-y^3-108y+18y^2.......................3

(4+y)^2=4^2+y^2+(2*4*y)
=16+y^2+8y..................................4


we know that .
3=4,
216-y^3-108y+18y^2=16+y^2+8y
(216-16)+(18y^2-y^2)=(8y+108y)+y^3
200+17y^2=216y+y^3
by solving the quadratic equation
we get
y=something and that way u will get x
i hopeit helps




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