Question

can u tell answers for which questions did u know

Answer 1

Step-by-step explanation:

5.

$\frac{1}{1 + \sqrt{2}} + \frac{1}{ \sqrt{2} + \sqrt{3}} = > \frac{( \sqrt{2} - 1) }{( \sqrt{2} + 1)( \sqrt{2} - 1)} +$

$\frac{( \sqrt{3} - \sqrt{2}) }{( \sqrt{3} + \sqrt{2})( \sqrt{3} - \sqrt{2})} = > \sqrt{2} - 1 + \sqrt{3} -$

$\sqrt{2} = > - 1 + \sqrt{3}$

4. a =>(3+√5)/2 and 1/a =>2/(3+√5)=>

2(3-√5)/(3+√5)(3-√5) =>(3-√5)2/4 =>(3-√5)/2

a+ 1/a => (3+√5)/2 +(3-√5)/2 =>3.

${(a + \frac{1}{a})}^{2} = {a}^{2} + \frac{1}{ {a}^{2}} + 2 = > 9 - 2 =$

${a}^{2} + \frac{1}{ {a}^{2}} = > {a}^{2} + \frac{1}{ {a}^{2} } = 7$

3.

$\sqrt[4]{81} \div 8 \sqrt[3]{216} + 15 \sqrt[5]{32} + \sqrt{225}$

Apply BODMAS rule

$3 \div 48 + 15 \times 2 + 15 = > \frac{1}{16} + 45 = >$

45.0625.

6. (i) x +1/x = 11 =>on squaring on both sides

${(x + \frac{1}{x}) }^{2} = {x}^{2} + \frac{1}{ {x}^{2}}+ 2.x. \frac{1}{x} = 121$

$= > {x}^{2} + \frac{1}{ {x}^{2}} = 121 - 2 = 119$

(ii)

${x}^{2} + \frac{1}{ {x}^{2}} = 4 = >$

On squaring on both sides, we get

${( {x}^{2} + \frac{1}{ {x}^{2} }) }^{2} = 16 = > {x}^{4} + \frac{1}{ {x}^{4}} + 2 =$

$16 = > {x}^{4} + \frac{1}{ {x}^{4}} = 16 - 2 = 14$

7. 3x+2y=20...(1) and 9x-y=11...(2) Multiply (1) by 2 and add to (2) => 3x+2y+2(9x-y)=20+

22 =>21x=42=>x=42/21=2. Substitute x=2 in the equation (1) =>3(2)+2y=20=>2y=20-6=14 =>y =14/2=7. We need to calculate the value of

$27 {x}^{3} + 8 {y}^{3} = > 27 {(2)}^{3} + 8 {(7)}^{3} = >$

$216 + 2744 = > 2960$

Hope it helps you.