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Step-by-step explanation:

27 ) 2x² - x - 1 = 0

2x² - 2x +  x  - 1 = 0

2x ( x - 1) + (x - 1) = 0

(x - 1)(2x + 1) = 0

x - 1 = 0  ; 2x + 1 = 0

x = 1   ;     2x = -1

                  x = -1/2

x = 1 ; -1/2

Option b

28) Area of a rectangle = 24 cm²

length * width = 24

(3x +2 )(2x -1) = 24

3x(2x -1) + 2(2x - 1) = 24

3x *2x - 3x *1 + 2*2x - 2*1 = 24

6x² -3x + 4x - 2= 24

6x² + x - 2 -24 = 0

6x² + x - 26 = 0

6x² -12x + 13x - 26 = 0

6x(x - 2) + 13(x - 2) = 0

(x -2)(6x +13) = 0

x = 2      {Ignore 6x + 13 as it gives negative value}

length = 3x + 2 = 3*2 + 2 = 6 + 2 = 8 cm

Width  = 2x - 1 = 2*2 - 1 = 4 - 1 = 3 cm

29) Area of square = 900 cm²

Side² = 900

(5x)² = 900

25x² = 900

x² = 900/25

x² = 36

x = √36 = √6*6

x = 6 cm

30) base = b cm

height = b + 2

Area of triangle =  24 cm²

b(b + 2) = 24*2

b² + 2b = 48

b² + 2b - 48 = 0

b²  - 6b + 8b  - 48 = 0

b(b - 6) + 8(b - 6) = 0

(b - 6) (b + 8) = 0

b - 6 = 0    {Ignore b +8 = 0 as it gives negative value}

b = 6 cm

height = 6+ 2 = 8 cm

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step-by-step explanation:

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