Find the value of: \((\sqrt{5} + 2)^2 - (\sqrt{5} - 2)^2\)
\(8\sqrt{5}\)
We must evaluate \((\sqrt{5} + 2)^2 - (\sqrt{5} - 2)^2\).
Use the identity \(a^2 - b^2 = (a + b)(a - b)\) with \(a = \sqrt{5} + 2\) and \(b = \sqrt{5} - 2\).
Then \(a + b = (\sqrt{5} + 2) + (\sqrt{5} - 2) = 2\sqrt{5}\).
And \(a - b = (\sqrt{5} + 2) - (\sqrt{5} - 2) = 4\).
Multiply the two results: \((2\sqrt{5}) \times 4 = 8\sqrt{5}\).
Alternatively, using \((x+y)^2 - (x-y)^2 = 4xy\) with \(x = \sqrt{5},\ y = 2\) gives \(4 \times \sqrt{5} \times 2 = 8\sqrt{5}\), confirming the answer.
Hence the value is \(8\sqrt{5}\).
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Important Questions from Identities
If x 2 + 4y 2 = 40, xy = 6 and x > 2y then the value of x - 2y is:
- \(\dfrac{(5.17-2.19)^2-(5.17+2.19)^2}{11.3223}\)
If a(a + b + c) 2= 1792; b(a + b + c) 2= 1536; c(a + b + c) 2= 768 then what will be the value of a?
If a + b + c = 5, a 2+ b 2+ c 2= 27, a 3 + b 3 + c 3 = 125, then the value of \(\frac{abc}{5}\) is:
(999) 2- 2 2=
