Question

If a+b=3 and ab=2 then find the value of (a-b)2

Answer 1

Step-by-step explanation:

(a-b)2 = (a+b) (a-b)

We have the value of a+b=3 and the value of ab=2.

We have to find the value of a-b=?

Let , a+b=3———(1) equation

ab=2——(2) equation

Now take eq. 1 and find the value of b, b=(3-a).

Put this value of b in the eq. (1) ,

a(3-a)=2

3a-a^2=2

a^2–3a+2=0, this is square equation so it has two value and when we factorized it we got,

a^2–2a-a+2=0

a(a-2)-1(a-2)=0

(a-1)(a-2)=0

It means that (a-1) & (a-2) both are the factors of a^2–2a-a+2.

We got two value of a =1 & 2

Condition 1. When a=1 then b=2

Condition 1. When a=1 then b=2Condition 2. When a=2 then b=1. Answer

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Answer 2

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We are aware of the identity

$(a - b)² = (a + b)² - 4ab$

$\implies \: (a - b)² = (3)² - 4 \times 2 = 9 - 8 = 1$

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