Question

(4-√7)(4+√7)
Solve the following

Answer 1

Answer:

23

Step-by-step explanation:

=(4-√7)(4+√7)

=(a - b)(a + b) = a'2 - b'2   by identity

=(4)'2 - (√7)'2

=16 + 7

=23

Answer 2

Your Answer:

The above Question is based on the application of algebraic identities

The algebraic identities Used is

$\tt \star \boxed{ (a+b)(a-b) = a^2-b^2 }$

Now here

$\boxed {\star a = 4} \\\\ \boxed{ \star \satr b = \sqrt7}$

Replacing values in above equation

$(4-\sqrt7)(4+\sqrt7) \\\\ \Rightarrow (4)^2- (\sqrt7)^2 \\\\ \Rightarrow 16 - 7\\\\ \Rightarrow 9$

So, answer is 9

Other Algebraic Formulas:

$\tt \star (a+b)^2 = a^2 + 2ab + b^2 \\\\ \tt \star (a-b)^2 = a^2 - 2ab +b^2 \\\\ \tt \star (a + b + c)^2 = a^2 + b^2 + c^2 + 2ab + 2bc + 2ca \\\\ \tt \star (a - b - c)2 = a2 + b2 + c2 - 2ab + 2bc - 2ca \\\\ \tt \star (a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3 = a^3 + b^3 + 3ab(a + b)$

Proving

$\tt \star \boxed{ (a+b)(a-b) = a^2-b^2 }$

$\tt (a-b)(a+b) \\\\ \tt = a(a+b) -b(a+b) \\\\ \tt = a^2 + ab - ab -b^2 \\\\ \tt = a^2-b^2$