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Conditional Identities

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Question

Try these problems on your own:

(i)

(ii)

(iii)

(iv)

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Solution

(i)

(ii)

(iii)

(iv)

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Now can you write the meaning of the expressions below in ordinary language?

(i)

(ii)

(iii)

(iv)

(v) x + y + 2

(vi)

(vii) ab + 1

(viii) (a + 1) (b + 1)

Now can you simplify these?

(i) (x + 4) + (x − 2)

(ii) (2x + 3) + (x − 1)

(iii) (x + 1) + (x − 1)

(iv) (5x + 6y) + (2x − 3y)

(v) (x + y) + (x − y)

Q. Question 1
Determine which of the following polynomials has (x+1) a factor:
(i)

x^{3} + x^{2} + x + 1

x^{4} + x^{3} + x^{2} + x + 1

x^{4} + 3 x^{3} + 3 x^{2} + x + 1

x^{3} - x^{2} - (2 + \sqrt{2}) x + \sqrt{2}

Q. Find a particular solution of each of the following differential equations:
(i)

(1 + x^{2}) \frac{d y}{d x} + 2 x y = \frac{1}{1 + x^{2}}; y = 0, when x = 1

(ii) (x + y) dy + (x − y) dx = 0; y = 1 when x = 1

(iii) x² dy + (xy + y²) dx = 0; y = 1 when x = 1

Q. Question 1
Determine which of the following polynomials has (x+1) a factor:
(i)

x^{3} + x^{2} + x + 1

x^{4} + x^{3} + x^{2} + x + 1

x^{4} + 3 x^{3} + 3 x^{2} + x + 1

x^{3} - x^{2} - (2 + \sqrt{2}) x + \sqrt{2}

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