Question

P-q = 7 ,pq= 9 then find p square +q squar

Answer 1

Solution:

It's given that, -

→ p - q = 7 and,

→ pq = 9

We have to find out the value of p² + q²

Concept:

• The given problem can be solved by using some algebraic identities.

Here,

→ p - q = 7

Squaring both sides, we get,

→ (p - q)² = 7²

→ (p - q)² = 49

Now, we know that,

→ (a - b)² = a² - 2ab + b²

Similarly,

→ (p - q)² = p² - 2pq + q²

→ p² + q² - 2pq = 49

We know that the value of pq is 9 ★

So,

→ p² + q² - 18 = 49

→ p² + q² = 67 which is our required answer.

Answer:

• p² + q² = 67.

Some Algebraic Identities:

• (a + b)² = a² + 2ab + b²
• (a - b)² = a² - 2ab + b²
• a² - b² = (a + b)(a - b)
• (a + b)² + (a - b)² = 4(a² + b²)
• (a + b)² - (a - b)² = 4ab
• (a + b)³ = a³ + 3ab(a + b) + b³
• (a - b)³ = a³ - 3ab(a - b) + b³
• a³ + b³ = (a + b)(a² - ab + b²)
• a³ - b³ = (a - b)(a² + ab + b²)

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