Question

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Answer 1

Ans 159)

Given :

a + b = 6  _____(i)

a = 6 - b

and , ab = 11 / 4 ___(ii)

(6 - b) (b) = 11 / 4

6b - b² = 11 / 4

b² - 6b +  11/4 = 0

b = 1/2 or b = 11/2

Putting in (i) equation :

a = 6 - 1/2  

a = 11/2

or

a = 6 - 11/2

a = 1/2    

To find : 2a³ - 2b³

Solution :

Case I : When a = 1/2 and b = 11/2 :

2 (1/2)³ - 2 (11/2)³ = 1/4 - 1331/4 = -1330/4 = - 665/2

Case II : When a = 11/2 and b = 1/2 :

2 (11/2)³ - 2 (1/2)³ = 1331/4 - 1/4 = 1330/4 = + 665/2

Ans 160)

Given : 3x + 4y = 16 ____(i)

xy = 4 ______(ii)

To find : 9x² + 16y²

Solution :

Squaring equation (i) from both sides :

(3x + 4y)² = 16²

9x² + 16y² + 24xy = 256

Putting value of xy in above equation we get :

9x² + 16y² + 96 = 256

9x² + 16y² = 256 - 96

9x² + 16y² = 160