Question

If a+b=9, ab=-22, find the value of (a-b)​

Answer 1

Answer:

Hey mate!

The answer is -13 or 13.

Step-by-step explanation:

Given:

a+b = 9 -----> (i)

ab = -22 -----> (ii)

From (i) a = 9-b

Putting the value of a in (ii)

(9-b)b = -22

$9b-b^{2}=-22\\ -b^{2}+9b+22=0\\-b^{2}+11b-2b+22=0\\-b(b-11) -2(b-11)=0\\(b-11)(-b-2)=0$

b-11=0         -b-2=0

b=11            -b=2

                  b=-2

∴ b=11 or b= -2

If b=11 then:

a = 9-b

a = 9-11

a = -2

If b= -2 then:

a = 9-b

a = 9-(-2)

a = 9+2

a = 11

Taking a = -2 and b = 11,

a-b = -2-11

a-b = -13

Taking a = 11 and b = -2,

a-b = 11-(-2)

a-b = 11+2

a-b = 13

∴ (a-b) = -13 or 13.

Hope this helps :)

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