Question

:
(i) If (4.x2 + xy) : (3xy - y2) = 12:5, find (x + 2y) : (2x + y)​

Answer 1

Answer:

(4x²+xy):(3xy-y²)=12:5

We can write it,

(4x²+xy)/(3xy-y²)=12/5

Now we can apply cross multiplication

5×(4x²+xy)=12×(3xy-y²)

20x²+5xy=36xy-12y²

20x²+12y²-31xy=0

Now we will divide by y on both sides,but since R.H.S is zero it will remain 0 only.

20(x²/y²)+12–31(x/y)=0

20(x/y)²-31(x/y)+12=0…..*

Now we will apply the quadratic formula,i.e.,

x=[-b±√(b²-4ac)]/2a

Now, in equation (*) a=20 , b=-31 , c= 12

(x/y)=[-(-31)±√{(-31)²-4×20×12}]/2×20

x/y=[31±√(961–960)]/40

x/y=[31±√1]/40

x/y=(31+1)/40 or (31–1)/40

x/y=32/40 or 30/40

x/y= 4/5 or 3/4

Therefore, there are two ratios for x:y,

x:y=4:5 or 3:4.

Step-by-step explanation:

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