Question

9) ifa + 2b = 5 and ab = 2, find a + 4bº1​

Answer 1

Answer:

9 or 6

Step-by-step explanation:

Given---> a + 2 b = 5 and ab = 2

To find---> Value of a + 4b

Solution---> ATQ, a + 2 b = 5 ..................(1)

ab = 2 ........................(2)

Now we solve these equations

a + 2b = 5

=> a = 5 - 2b

Putting a = 5 - 2b in equation ( 1 ) , we get,

=> ( 5 - 2b ) b = 2

Multiplying by b in to bracket , we get,

=> 5 b - 2 b b = 2

=> 5 b - 2 b² = 2

=> - 2 b² + 5 b - 2 = 0

Chabging the sign of whole equation , we get,

=> 2b² - 5b + 2 = 0

Now we factorize it by splitting the middle term

=> 2b² - ( 4 + 1 ) b + 2 = 0

=> 2b² - 4b - b + 2 = 0

=> 2b ( b - 2 ) - 1 ( b - 2 ) = 0

=> ( b - 2 ) ( 2b - 1 ) = 0

If, b - 2 = 0

=> b = 2

Now a = 5 - 2 b

a = 5 - 2 ( 2 )

a = 5 - 4

a = 1

So , a + 4b = 1 + 4 ( 2 )

= 1 + 8

a + 4 b = 9

If , 2 b - 1 = 0

=> 2 b = 1

=> b = 1 / 2

a = 5 - 2b

= 5 - 2 ( 1 / 2 )

= 5 - 1

a = 4

Now , a + 4b = 4 + 4 ( 1 / 2 )

= 4 + 2

= 6

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