Question

if a+b =4 and a×b= 2 then a-b=?​

Answer 1

Answer:

$\large\boxed{\bigstar\:\:a-b=2\sqrt{2}\:\:\bigstar }$

Step-by-step explanation:

✧ Given:-

• a+b=4
• a×b=2

✧ To Find:-

   Value of (a-b).

✧ Formula Applied:-

• (a+b)²=a²+b²+2ab
• (a-b)²=a²+b²-2ab

✧ Solution:-

⇒ (a+b)²=a²+b²+2ab

⇒ (a-b)²= a²+b²-2ab+2ab-2ab

⇒ (a-b)²= a²+b²+2ab-4ab

⇒ (a-b)²=(a+b)²-4ab              [∵ (a+b)²=a²+b²+2ab]

⇒ (a-b)²=(4)²-4(2)                  [∵ (a+b)=4 and ab=2]

⇒ (a-b)²=16-8

⇒ (a-b)²=8

$\implies (a-b)=\sqrt{8}$

$\implies\boxed{a-b=2\sqrt{2} }$