Determine the value of ‘a’ which satisfies the equation: \({9^{\sqrt a }} + {40^{\sqrt a }} = {41^{\sqrt a }}.\)?

1
2
3
4

LohaHridoy

4 views

2025-01-04 04:42

1 Answers

AhmedNazir

Option 4 : 4

Let x = √a

Hence, we can write,

⇒ 9^x + 40^x = 41^x

Putting x = 1,

⇒ 9¹ + 40¹= 9 + 40 = 49 ≠ 41¹

Putting x = 2,

⇒ 9² + 40²= 81 + 1600 = 1681 = 41²

⇒ x = √a = 2

⇒ a= 2²

∴ a = 4

4 views Answered 2022-09-04 04:29

Related Questions

Look at the given equation and determine which symbol should come in place of question mark to correct the equation. 37 6 + (14 – 6) ÷ 2 – 7 + 45 ÷ 5 × 4 + 49 = 304?

1 Answers 4 Views

A person of height 2 meters wants to get a book which is on a cupboard of height \(\frac{{1 + \sqrt 3 }}{{2\sqrt 3 }}\) meters. If he stands at a distance of (1 - 3√3) meters from the foot of the cupboard, then the angle at which he should use stick, so that it hits the book is?

1 Answers 5 Views

Determine the value of ‘r’ for which the equation 13x + 5 = rx + 18 has no solution.?

1 Answers 8 Views

Which of the following statement(s) is/are TRUE I. \(\frac{2}{{3\sqrt 5 }} < \frac{3}{{2\sqrt 5 }} < \frac{5}{{4\sqrt 3 }}\) II. \(\frac{3}{{2\sqrt 5 }} < \frac{2}{{3\sqrt 3 }} < \frac{7}{{4\sqrt 5 }}\) ?

1 Answers 4 Views

Which of the following statement(s) is/are TRUE I. \(\sqrt {324} + \sqrt {3.24} + \sqrt {0.0324} = 19.98\) II. \(\sqrt {129 + \sqrt {121} + \sqrt {361} + \sqrt {100} } = 13\)?

1 Answers 4 Views

Which of the following is TRUE \({\rm{I}}.{\rm{\;}}\sqrt[3]{{11}} > \sqrt 7 > \sqrt[4]{{45}}\) \({\rm{II}}.{\rm{\;}}\sqrt 7 > \sqrt[3]{{11}} > \sqrt[4]{{45}}\) \({\rm{III}}.{\rm{\;}}\sqrt 7 > \sqrt[4]{{45}} > \sqrt[3]{{11}}\) \({\rm{IV}}.{\rm{\;}}\sqrt[4]{{45}} > \sqrt 7 > \sqrt[3]{{11}}\)?

1 Answers 4 Views

Which of the following value of ‘x + y’ satisfies the equation 4(x – 1) 9(2y – 8) = 5184?

1 Answers 4 Views

The value of x which satisfies the equation 5(1 + x) + 5(1 – x) = 26 are?

1 Answers 4 Views

Which of the following statement(s) is/are TRUE (I) \(\sqrt {144} \times \sqrt {36} < \sqrt[3]{{125}} \times \sqrt {121}\) (II) \(\sqrt {324} + \sqrt {49} > \sqrt[3]{{216}} \times \sqrt 9\)?

1 Answers 4 Views

Which value among \(\sqrt[3]{5},\sqrt[4]{6},\;\sqrt[6]{{12}},\sqrt[{12}]{{276}}\) is the largest?

1 Answers 4 Views

এক্সাম দিয়ে মেধা যাচাই করুন

Job Preparation (1125)

Admission (754)

এসএসসি (10)

এইচএসসি (5)