Question

If (x^2+3x+5)*(x^2-3x+5)=m^2 - n^2, then m = ______.

Answer 1

Given:-

• (x² + 3x + 5) * (x² - 3x + 5) = m² - n²

To find:-

• The value of m

Answer:-

Given that,

(x² + 3x + 5) * (x² - 3x + 5) = m² - n²

We shall write it as,

→ (x² + 5 + 3x) * (x² + 5 - 3x) = m² - n²

→ {(x² + 5) + 3x)} * {(x² + 5) - 3x)} = m² - n²

• It is now in the form of (a + b)(a + b), with a = (x² + 5) and b = 3x
• We know that, (a + b)(a - b) = a² - b²

→ (x² + 5)² - (3x)² = m² - n²

Now, by comparing both sides, we can say that,

→ m = x² + 5 Ans

and n = 3x

Extra knowledge:-

• (a + b)² = a² + b² + 2ab
• (a - b)² = a² + b² - 2ab
• a² - b² = (a + b)(a - b)
• (a + b)³ = a³ + b³ + 3ab(a + b)
• (a - b)³ = a³ - b³ - 3ab(a - b)
• a³ + b³ = (a + b)(a² + b² - ab)
• a³ - b³ = (a - b)(a² + b² + ab)
• (a + b + c)² = a² + b² + c² + 2(ab + bc + ca)
• a³ + b³ + c³ - 3abc = (a + b + c)(a² + b² + c² - ab - bc - ca)