Math, asked by singhvedantrajput122, 1 month ago

simplify (√5 + √2)(√5 -√2)​

Answers

Answered by manvibaghel07
1

Answer:

3

Step-by-step explanation:

We use formula

 {a}^{2}  -  {b}^{2}  = (a  + b)(a - b)

(√5+√2)(√5-√2) = (√5)^2 - (√2)^2

= 5-2

= 3

so, simplify solutions is 3.

Answered by ChikkukiAshee
2

Answer:

 \large \sf{ \underline{ \underline{ \purple{ \dag{Question}}}}}

Simplify :

  \large\bf( \sqrt{5}  +  \sqrt{2} )( \sqrt{5}  -  \sqrt{2)}

 \large \sf{ \underline{ \underline{ \blue{ \dag{Answer}}}}}

 \large \sf{ \underline{To \: find : }}

  \large\bf( \sqrt{5}  +  \sqrt{2} )( \sqrt{5}  -  \sqrt{2)}

 \large \sf{ \underline{Identity \: used : }}

 \large \sf \: (a + b)(a - b) =  {a}^{2}  - b {}^{2}

 \large \sf{ \underline{{Solⁿ :}}}

 \large \bf\implies ( \sqrt{5}  +  \sqrt{2} )( \sqrt{5}  -  \sqrt{2)}

 \large \bf =(  \sqrt{5})^{2} - ( \sqrt{2 }) {}^{2}

 \large \bf = 5 - 2

 \large \bf = 3

Hence, the simplified solution is 3.

 \large \sf{ \underline{ \pink{Some  \: other  \: algebraic \:  Identities :}}}

 \large \sf \:❥(a + b)(a - b) =  {a}^{2}  - b {}^{2}

 \large \sf \:❥(a + b) {}^{2}  =  {a}^{2}  + 2ab + b {}^{2}

 \large \sf \:❥(a  - b) {}^{2}  =  {a}^{2}   -  2ab + b {}^{2}

 \large \sf \:❥(x +a ) (x + b) = x {}^{2}  + (a + b)x + ab

 \large \sf \:❥ \: a{}^{2}  + b {}^{2}  = (a + b) {}^{2}  - 2ab

 \large \sf \:❥ \: x{}^{3}  + y {}^{3}  = (x + y)(x {}^{2}  - 2xy + y {}^{2} )

\large \sf \:❥ \: x{}^{3}   -  y {}^{3}  = (x  -  y)(x {}^{2}   +  2xy + y {}^{2} )

\large \sf \:❥ \: (x + y) {}^{3} =x {}^{3}  + y {}^{3}  + 3xy(x + y)

\large \sf \:❥ \: (x  -  y) {}^{3} =x {}^{3}  - y {}^{3}   - 3xy(x  -  y)

\large \sf \:❥ \: (x  + y + z) {}^{2}  = x {}^{2}  + y {}^{2}  + z {}^{2}  + 2xy + 2yz + 2zx

\large \sf \:❥ \: x^{3}  + y^{3}  +  {z}^{2}  - 3xyz = (x + y + z)({x}^{2}  +  {y}^{2}  +  {z}^{2}  - xy - yz - zx)

 \large \sf{ \red{Hope \:  it  \: helps...}}

 \huge {\underline{{ \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \: }}}

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