Question

If (a + b)2
– 2(a + b) = 80 and ab = 16, then what can be the value of 3a – 19b?

Answer 1

here is your ans..........

Answer 2

When a=2 and b=8 then $3a-19b=-14$.

When a=8 and b=2 then $3a-19b=-146$.

Step-by-step explanation:

Given : If $(a+b)^2-2(a+b)=80$ and $ab=16$.

To find : What can be the value of $3a-19b$ ?

Solution :

$(a+b)^2-2(a+b)=80$

Add square of 1 both side,

$(a + b)^2-2(a + b) +(1)^2 = 80+(1)^2$

$(a + b-1)^2= 81$

Taking root both side,

$a + b-1 = 9$

$a + b = 10$   ....(1)

Consider $ab=16$ ....(2)

Substitute the value of a from (1) in (2),

$(10-b)b=16$

$b^2-10b+16=0$

$b^2-8b-2b+16=0$

$b(b-8)-2(b-8)=0$

$(b-8)(b-2)=0$

$b=8,2$

When b=2,

a+2=10

a=8

The value is $3a-19b=3(8)-19(2)=24-38=-14$

When b=8,

a+8=10

a=2

The value is $3a-19b=3(2)-19(8)=6-152=-146$

#Learn more

(a^2+b^2) (a^2+b^2)-(a^2-b^2) (a^2-b^2)​

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