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If $straight a space equals space square root of 2 space plus space 1 comma space space space straight b space equals space square root of 2 space minus space 1 comma$ then the value of $fraction numerator 1 over denominator straight a plus 1 end fraction space plus space fraction numerator 1 over denominator straight b plus 1 end fraction$ is

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162.

If a³ - b³ = 56 and a - b = 2, then what is the value of a² + b²?

164 Views

163.

If x² - 3x + 1 = 0, $left parenthesis straight x space not equal to space 0 right parenthesis comma$ then the value of $straight x space plus space 1 over straight x$ is

52 Views

164.

If $fraction numerator 2 plus straight a over denominator straight a end fraction space plus space fraction numerator 2 plus straight b over denominator straight b end fraction space plus space fraction numerator 2 plus straight c over denominator straight c end fraction space equals space 4 comma$ then the value of $fraction numerator ab plus bc plus ca over denominator abc end fraction$ is:

2
1
0
$1 half$

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165.

If $straight x space plus space straight y plus space straight z space equals space 1 comma space space$ $1 over straight x plus 1 over straight y plus 1 over straight z space equals space 1$ and xyz = -1, then x³ + y³ + z³ is equal to:

-1
1
-2
2

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166.

The value of $fraction numerator straight a over denominator straight a minus straight b end fraction space plus space fraction numerator straight b over denominator straight b minus straight a end fraction$ is

$fraction numerator left parenthesis straight a plus straight b right parenthesis over denominator left parenthesis straight a minus straight b right parenthesis end fraction$
-1
2ab
1

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167.

If $4 straight x space equals space square root of 5 space plus space 2 comma$ then the value of $straight x minus fraction numerator 1 over denominator 16 straight x end fraction$

1
-1
4
$2 square root of 5$

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168.

If $straight x space equals space fraction numerator 1 over denominator left parenthesis square root of 2 plus 1 right parenthesis end fraction comma$ then the value of x² + 2x - 1 is

$2 square root of 2$
4
0
3

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169.

If $straight x space plus space 1 over straight x space equals space 6 comma$ then the value of $straight x squared space plus space 1 over straight x squared$ is:

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170.
If a(x + y) = b(x - y) = 2ab, the the value of 2(x² + y²) is

2 (a² - b²)

2(a² + b²)

4(a² - b²)

4(a² + b²)

4(a² + b²)

a(x + y) = b(x - y) = 2ab
a(x + y) = 2ab
$straight b space equals space fraction numerator straight x plus straight y over denominator 2 end fraction$
2b = x + y .... (i)
b(x - y) = 2ab
$straight a space equals space fraction numerator left parenthesis straight x space space minus space straight y right parenthesis over denominator 2 end fraction$
2a = x - y ...(ii)
Solving (i) and (ii), we get
x = a + b, y = b - a
∴ 2(x² + y²) = 2[(a + b)]² + (b - a)²]
= 2[a² + b² + 2ab + b² + a² - 2ab]
= 2[2a² + 2b²]
= 4(a² + b²)