Question

simplify (√5 + √2)(√5 -√2)​

Answer 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.

Answer 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.

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

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

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

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

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

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

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

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

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

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

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

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

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

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