Maths lovers solve this if you can!!!!!!!
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Here ,
√3 + ³ √5
Let x =√3
y = ³√5
x^6 = (√2)^6 = (2)³ = 8
y^6 = (³√5)^6 = (5)² = 25
we know , for rationalize we have require (x + y) .
convert x^6 + y^6 to in such a way that here (x + y) must include.
x^6 + y^6 = x^6 +x^5y - x^5y - x^4y² + x⁴y² + x³y³ - x³y³ - x²y⁴ + x²y⁴ + xy^5 - xy^5 - y^6
= x^5( x + y) - x^4y( x + y) + x^3y²( x + y) -x²y³( x + y) + xy⁴(x + y) - y^5(x + y)
= (x + y) { x^5 -x⁴y + x³y² -x²y³ + xy⁴ - y^5 }
now,
x^6 + y^6 = 8 + 25 = 33
( x + y) { x^5 -x⁴y + x³y² - x²y³ + xy⁴ - y^5} = 33
put x = (2)½ and y = (5)⅓ in { x^5 - x⁴y+ x³y² - x²y³ + xy⁴ - y^5 }
and then , 33 divide by it .
then, you got ( x + y)
here , (x + y) is rationalize of √3 + ³√5
hence, {x^5 - x⁴y + x³y² -x²y³ + xy⁴ - y^5 } is rationalise factor where x = (2)½ and y = (5)⅓
√3 + ³ √5
Let x =√3
y = ³√5
x^6 = (√2)^6 = (2)³ = 8
y^6 = (³√5)^6 = (5)² = 25
we know , for rationalize we have require (x + y) .
convert x^6 + y^6 to in such a way that here (x + y) must include.
x^6 + y^6 = x^6 +x^5y - x^5y - x^4y² + x⁴y² + x³y³ - x³y³ - x²y⁴ + x²y⁴ + xy^5 - xy^5 - y^6
= x^5( x + y) - x^4y( x + y) + x^3y²( x + y) -x²y³( x + y) + xy⁴(x + y) - y^5(x + y)
= (x + y) { x^5 -x⁴y + x³y² -x²y³ + xy⁴ - y^5 }
now,
x^6 + y^6 = 8 + 25 = 33
( x + y) { x^5 -x⁴y + x³y² - x²y³ + xy⁴ - y^5} = 33
put x = (2)½ and y = (5)⅓ in { x^5 - x⁴y+ x³y² - x²y³ + xy⁴ - y^5 }
and then , 33 divide by it .
then, you got ( x + y)
here , (x + y) is rationalize of √3 + ³√5
hence, {x^5 - x⁴y + x³y² -x²y³ + xy⁴ - y^5 } is rationalise factor where x = (2)½ and y = (5)⅓
Answered by
1
Answer:
Here,
3 V3 + V5 Let x =V3 y = 3V5
x^6 = (V2)^6 = (2)³ = 8 = = y^6 = ( 5)^6 = (5)2 = 25
we know , for rationalize we have require (x + y).
convert x^6 + y^6 to in such a way that here (x + y) must include.
x^6 + y^6 = x^6 +x^5y - x^5y - x^4y² + x*y? 3,3 +x°y³ - x°y³ - x²y + x?y* + xy^5 - xy^5 - y^6
= x^5( x + y) - x^4y( x + y) + x^3y2(x + y) - x?y3(x + y) + xy 4(x + y) - y^5(x + y)
= (x + y) { x^5 -x*y +x°y? -x?y³ + xy* - y^5}
now, x^6 + y^6 = 8 + 25 = 33
(x+ y){x^5 -x*y + x°y? - x²y³ + xy* -y^5} = 33
put x = (2)½ and y = (5)73 in { x^5 - x*y+ x³y? - xy + xy* - y^5} and then , 33 divide by it.
then, you got (x+y)
here , (x + y) is rationalize of v3 + 3V5
hence, {x^5 - x*y+ x³y? -x?y³ + xy* - y^5 } is rationalise factor where x = (2)2 and y = (5)3
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