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Solution of Linear Equation in 2 Variables

Find 1+x y+x ...

Question

Find 1 + (xy) + (xy)² + (xy)³ + …… if a= 1+ 2x + 3x² + 4x³+….. ( -1<a<1) and b= 1+3y + 6y² + 10y³+…. (-1<b<1)

A

(a^1/2b^1/3) / (a^1/2 + b^1/3 -1)

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B

(a^1/2b^1/3) / (a^1/2 + b^1/3 +1)

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C

(a^1/2 + b^1/3 +1) / (a^1/2b^1/3)

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D

(a^1/2 + b^1/3 -2) / (a^1/2b^1/3)

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E

(a^1/2 + b^1/3 +2) / (a^1/2b^1/3)

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Solution

The correct option is A (a^1/2b^1/3) / (a^1/2 + b^1/3 -1)
Option (a)
Assume x=0 and y=0. Then the equation gives a value of 1. Put the values of x
and y to get a and b. a=1 and b=1
Go from answer options. Only answer option a gives 1

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Similar questions

∣ x ∣< 1

∣ y ∣< 1

(x + y) + (x^{2} + x y + y^{2}) + (x^{3} + x^{2} y + x y^{2} + y^{3}) + . . . . . \infty

| x | < 1, | y | < 1

x \neq y,

then the sum to infinity of the following series

(x + y) + (x^{2} + x y + y^{2}) + (x^{3} + x^{2} y + x y^{2} + y^{3}) + . . . . . . \infty

If $| x | < 1$ and $| y | < 1,$ find the sum to infinity of the series

$(x + y) + (x^{2} + x y + y^{2}) + (x^{3} + x^{2} y + x y^{2} + y^{3}) + . . . .$

Or

Find the sum to n terms of the series $\frac{1}{1.3} + \frac{1}{3.5} + \frac{1}{5.7} + . . . .$

X Y_{3}

decomposes as :
The ratio of partial pressure of

X Y

X Y_{2}

in the mixture of gases obtained by decomposition of

X Y_{3}

(g) is 2 : 1. Find the total enthalpy change for the decomposition of 1 mole of

X Y_{3}

.

1 + (x y) + (x y)^{2} + (x y)^{3} + . . . .

a = 1 + 2 x + 3 x^{2} + 4 x^{3} + . . . . (- 1 < a < 1)

b = 1 + 3 y + 6 y^{2} + 10 y^{3} + . . . (- 1 < b < 1)

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