If x = 7 + 4√3, find the value of x^4 + (1/x^4).
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Answer:Hey mate !
_______________________
Given :
x = 7 + 4√3
To find :
√x + 1 / √x
Solution :
x = 7 + 4√3
⇒ x = 4 + 3 + 4√3
⇒ x = 2² + √3² + 2 × 2 × √3
⇒ x = ( 2 + √3)²
⇒ √x = 2 + √3
Now,
1 / √x = 1 / 2 + √3 × 2 - √3 / 2 - √3
⇒ 1 / √x = 2 - √3 / 2² - √3²
⇒ 1 / √x = 2 - √3 / 4 - 3
⇒ 1 / √x = 2 - √3
Again,
√x + 1 / √x = 2 + √3 + 2 - √3
⇒ √x + 1 / √x = 2 + 2
⇒ √x + 1 / √x = 4
Hence,
√x + 1 / √x = 4
√
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If x = 7 + 4√3, find the value of x^4 + (1/x^4).
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HCF (306, 657) = 9 दिया है। LCM (306, 657) ज्ञात कीजिए:
Answer:
x=7+4√3
1/x=1/7+4√3
=1/7+4√3×7-4√3/7-4√3
=7-4√3/1
=7-4√3
x^4+1/x^4
=(7+4√3)^4+(7-4√3)^4
=((7+4√3)^2)^2 +((7-4√3)^2)^2
=(97+56√3)^2+ (97-56√3)^2
=2((97)^2+(56√3)^2)
=2(9409+9408)
=37,634
x^4+1/x^4 =37,634
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