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Examples 1 to 3

July 22, 2020
Category: Examples 1 to 3

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Examples :

(1) Solve the equations :

(i) 3x² + 5x + 2 = 0

(ii) 3x² – 5x + 2 = 0

(iii) 3x² + 5x – 2 = 0

(iv) 3x² – 5x – 2 = 0

(i) 3x² + 5x + 2 = 0

$\therefore$ 3x² + 3x + 2x + 2 = 0

$\therefore$ 3x ( x + 1) + 2 ( x + 1 ) = 0

$\therefore$ ( x + 1) ( 3x + 2 ) = 0

$\therefore$ x + 1 = 0 or 3x + 2 = 0

$\therefore$ x = – 1 or x = $- \frac{2}{3}$

$\therefore$ S. S. = $\left \{ -1, -\frac{2}{3} \right \}$

(ii) 3x² – 5x + 2 = 0

$\therefore$ 3x² – 3x – 2x + 2 = 0

$\therefore$ 3x ( x – 1) – 2 ( x – 1 ) = 0

$\therefore$ ( x – 1) ( 3x – 2 ) = 0

$\therefore$ x – 1 = 0 or 3x – 2 = 0

$\therefore$ x = 1 or x = $\frac{2}{3}$

$\therefore$ S. S. = $\left \{ \frac{2}{3}, 1 \right \}$

(iii) 3x² + 5x – 2 = 0

$\therefore$ 3x² + 6x – x – 2 = 0

$\therefore$ 3x ( x + 2) – 1 ( x + 2 ) = 0

$\therefore$ ( x + 2) ( 3x – 1 ) = 0

$\therefore$ x + 2 = 0 or 3x – 1 = 0

$\therefore$ x = – 2 or x = $\frac{1}{3}$

$\therefore$ S. S. = $\left \{ -2, -\frac{1}{3} \right \}$

(iv) 3x² – 5x – 2 = 0

$\therefore$ 3x² – 6x + x – 2 = 0

$\therefore$ 3x ( x – 2) + 1 ( x – 2 ) = 0

$\therefore$ ( x – 2) ( 3x + 1 ) = 0

$\therefore$ x – 2 = 0 or 3x + 1 = 0

$\therefore$ x = 2 or x = – $\frac{1}{3}$

$\therefore$ S. S. = $\left \{- \frac{1}{3}, 2 \right \}$

(2) Solve the equations :

(i) x² + 5x + 6 = 0

(ii) x² – 5x + 6 = 0

(iii) x² + 5x – 6 = 0

(iv) x² – 5x – 6 = 0

(i) x² + 5x + 6 = 0

$\therefore$ ( x + 2) (x + 3 ) = 0

$\therefore$ x + 2 = 0 or x + 3 = 0

$\therefore$ x = – 2 or x = – 3

$\therefore$ S.S. = { – 2, – 3 }

(ii) x² – 5x + 6 = 0

$\therefore$ ( x – 2) (x – 3 ) = 0

$\therefore$ x – 2 = 0 or x – 3 = 0

$\therefore$ x = 2 or x = 3

$\therefore$ S.S. = { 2, 3 }

(iii) x²+ 5x – 6 = 0

$\therefore$ ( x + 6) (x – 1 ) = 0

$\therefore$ x + 6 = 0 or x – 1 = 0

$\therefore$ x = – 6 or x = 1

$\therefore$ S. S. = { – 6, 1 }

(iv) x² – 5x – 6 = 0

$\therefore$ ( x – 6) (x + 1 ) = 0

$\therefore$ x – 6 = 0 or x + 1 = 0

$\therefore$ x = 6 or x = – 1

S. S. = { – 1, 61 }

(3) Solve : x⁴ – 10x² + 9 = 0.

Soln. x⁴ – 5x² + 4 = 0

$\therefore$ y² – 5y + 4 = 0

$\therefore$ ( y – 4) (y – 1 ) = 0

$\therefore$ y – 4 = 0 or y – 1 = 0

$\therefore$ y = 4 $\therefore$ y = 1

$\therefore$ x² = 4 $\therefore$ x² = 1

$\therefore$ x = 2 x = 1

$\therefore$ S. = { $\pm$ 1, $\pm$ 2 }

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Examples 1 to 3

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