ID#3840 BCS General Math Preli (40)
MS Word Writing Guide
১.
প্রথমে উপরের COPY বাটনে ক্লিক করুন।
২.
MS Word-এ গিয়ে Ctrl + V দিয়ে পেস্ট করুন।
৩.
সমীকরণটি সিলেক্ট করে কিবোর্ডে Alt + = চাপুন।
Shortcut: Alt and equal key
৪.
এরপর ডানদিকের ড্রপডাউন থেকে Professional সিলেক্ট করলেই গণিত সুন্দর দেখাবে।
$x^4-x^2+1=0$ হয়, তবে $x^3+\frac{1}{x^3} =$ কত?
ক) 3
খ) √3
গ) 2
ঘ) 0
ঘ
ব্যাখ্যা
Step 1: Find the value of x + 1/x
Given equation: x⁴ - x² + 1 = 0
Dividing both sides by x²:
(x⁴ / x²) - (x² / x²) + (1 / x²) = 0
x² - 1 + 1/x² = 0
x² + 1/x² = 1
Using the formula a² + b² = (a + b)² - 2ab:
(x + 1/x)² - 2(x)(1/x) = 1
(x + 1/x)² - 2 = 1
(x + 1/x)² = 3
x + 1/x = √3
Step 2: Find the value of x³ + 1/x³
Using the formula a³ + b³ = (a + b)³ - 3ab(a + b):
x³ + 1/x³ = (x + 1/x)³ - 3(x)(1/x)(x + 1/x)
Substituting (x + 1/x) = √3:
x³ + 1/x³ = (√3)³ - 3(√3)
x³ + 1/x³ = 3√3 - 3√3
x³ + 1/x³ = 0
Answer: 0
Given equation: x⁴ - x² + 1 = 0
Dividing both sides by x²:
(x⁴ / x²) - (x² / x²) + (1 / x²) = 0
x² - 1 + 1/x² = 0
x² + 1/x² = 1
Using the formula a² + b² = (a + b)² - 2ab:
(x + 1/x)² - 2(x)(1/x) = 1
(x + 1/x)² - 2 = 1
(x + 1/x)² = 3
x + 1/x = √3
Step 2: Find the value of x³ + 1/x³
Using the formula a³ + b³ = (a + b)³ - 3ab(a + b):
x³ + 1/x³ = (x + 1/x)³ - 3(x)(1/x)(x + 1/x)
Substituting (x + 1/x) = √3:
x³ + 1/x³ = (√3)³ - 3(√3)
x³ + 1/x³ = 3√3 - 3√3
x³ + 1/x³ = 0
Answer: 0
Resource Details
| Exam | BCS |
| Subject | General Math |
| Chapter | 12 |
| Year | 40 |
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