Question

Solve : (3+√5 )(3-√5 ) – 4​

Answer 1

$\underline{ \underline{ \Large \pmb{\sf { {Given \: Expression:}} }} }$

• $\sf { (3+ \sqrt{5}) ( 3 - \sqrt{5}) - 4}$

$\underline{ \underline{ \Large \pmb{\sf { {Required \: Solution:}} }} }$

Here, we are given an expression and we have to simplify the expression containing square roots. We can easily solve this question by using identities for indices.

Identity we have to use here :

$\bigstar \: \boxed{ \sf { (a+ \sqrt{b}) ( a - \sqrt{b}) = {a}^{2} - b }}$

Here,

• $\sf { (3+ \sqrt{5}) ( 3 - \sqrt{5}) - 4}$

✰ a = 3

✰ b = 5

By using this identity,

$\longrightarrow \sf {( 3^2 - 5) - 4 }$

Finding the square of 3 and subtracting 5 from the square of 3.

$\longrightarrow \sf {( 9 - 5) - 4 }$

$\longrightarrow \sf {4 - 4 }$

$\longrightarrow \boxed{ \pmb {\rm \red {0 }}}$

Therefore, ( 3 + √5 )( 3 - √5 ) – 4 is 0.

⠀⠀⠀⠀⠀_____________

$\underline{ \underline{ \Large \pmb{\sf { {More \: identities :}} }} }$

$\small \boxed{ \begin{array}{cc} { \sf{ \star \: \: {( \sqrt{a} )}^{2} = a } } \\ \\ \star \: \: \sf \sqrt{a} \sqrt{b} = \sqrt{ab} \\ \\ \star \: \: \sf \dfrac{ \sqrt{a} }{ \sqrt{b} } = \sqrt{ \dfrac{a}{b} } \\ \\ \star \: \: \sf( \sqrt{a} + \sqrt{b} )( \sqrt{a} - \sqrt{b} ) = a - b \\ \\ \star \: \: \sf( \sqrt{a} \pm \sqrt{b} ) {}^{2} = {a}^{2} \pm2 \sqrt{ab} + b \\ \\ \star \: \: \sf{ (a + \sqrt{b})(a - \sqrt{b} ) = {a}^{2} - b } \end{array}}$

Answer 2

Step-by-step explanation:

Identity we have to use here :

(a+✓b)(a-✓b) = a²- b

Here,

✰ a = 3

✰ b = 5

By using this identity,

(3+✓5)(3-✓5)-4

(3²-5)-4

Finding the square of 3 and subtracting 5 from the square of 3.

Therefore, ( 3 + √5 )( 3 - √5 ) – 4 is 0.

hopefully it will work ☺️☺️