if $ P^2 + 1 P^2 = 7$ , then find the value of $ P^2 - 1 P^2 .$

খ) $3 5$ — $ & ( a + b )^2 = ( a - b )^2 + 4ab & \ \ \ \ \ ( P + 1 P )^2 = ( P - 1 P )^2 + 4 $ Given expression: $ \ \ \ \ P^2 + 1 P^2 = 7$ -------------- (1) Subtracting 2 from both sides, we get: $ & \ \ \ \ P^2 + 1 P^2 - 2 = 7 - 2 & \ \ \ \ \ ( P - 1 P )^2 = 5 $ $ \ \ \ \ \ P - 1 P = 5$ -------------- (2) Now adding 2 to both sides in equation (1) we get, $ & \ \ \ \ \ P^2 + 1 P^2 + 2 = 7 + 2 & \ \ \ \ ( P + 1 P )^2 = 9 $ $ P + 1 P = 3$ -------------- (3) Formula: - $ ( a + b ) ( a - b ) = ( a^2 - b^2 )$ Now, multiplying equations (2) and (3) we get, $ & \ \ \ \ ( P + 1 P ) ( P - 1 P ) = 3 5 & \ \ \ \ P^2 - 1 P^2 = 3 5 $

if $ P^2 + 1 P^2 = 7$ , then find the v… | Answer

Subject

Quantitative Aptitude

Topic

Algebra

if ${P^2} + {1 \over {{P^2}}} = 7$ , then find the value of ${P^2} - {1 \over {{P^2}}}.$
Reading

ক)

$2\sqrt 5$

খ)

$3\sqrt 5$

গ)

$4\sqrt 5$

ঘ)

$5\sqrt 5$

ঙ)

None of these

Explanation

\eqalign{ & {\left( {a + b} \right)^2} = {\left( {a - b} \right)^2} + 4ab \cr & \Rightarrow\ \ \ \ \ {\left( {P + {1 \over P}} \right)^2} = {\left( {P - {1 \over P}} \right)^2} + 4 \cr} Given expression:

\Rightarrow\ \ \ \ {P^2} + {1 \over {{P^2}}} = 7

-------------- (1) Subtracting 2 from both sides, we get: \eqalign{&\Rightarrow\ \ \ \ {P^2} + {1 \over {{P^2}}} - 2 = 7 - 2 \cr &\Rightarrow\ \ \ \ \ {\left( {P - {1 \over P}} \right)^2} = 5 \cr}

\Rightarrow\ \ \ \ \ P - {1 \over P} = \sqrt 5

-------------- (2) Now adding 2 to both sides in equation (1) we get, \eqalign{ & \Rightarrow\ \ \ \ \ {P^2} + {1 \over {{P^2}}} + 2 = 7 + 2 \cr & \Rightarrow\ \ \ \ {\left( {P + {1 \over P}} \right)^2} = 9 \cr}

\Rightarrow P + {1 \over P} = 3

-------------- (3) Formula: -

\left( {a + b} \right)\left( {a - b} \right) = \left( {{a^2} - {b^2}} \right)

Now, multiplying equations (2) and (3) we get, \eqalign{ & \Rightarrow\ \ \ \ \left( {P + {1 \over P}} \right)\left( {P - {1 \over P}} \right) = 3\sqrt 5 \cr & \Rightarrow\ \ \ \ {P^2} - {1 \over {{P^2}}} = 3\sqrt 5 \cr}

\frac{a}{3} = \frac{b}{4} = \frac{c}{7}

then what would be the value of

\frac{{a + b + c}}{a}

?Multiplication and difference of two numbers are 93 and 28 respectively. Find the difference of reciprocals of the numbers.In following question, two equations are given, you have to solve them and choose the correct option: x2– 3x – 4 = 0, y2– 4 = 0 In following question, two equations are given, you have to solve them and chose the correct option: x2+ 11x + 30 = 0, y2+ 7y + 12 = 0 In the following question, one or two equation(s) is/are given. You have to solve both the equations and find the relation between ‘l’ and ‘m’ and mark correct answer. I. (125)1/3l – (1331)1/3= 4 × (729)1/6+ (1024)1/10II. (m)2– (15625)1/3= 0 Direction: In the following question two equations numbered I and II are given. You have to solve both the equations and give answers:I: x - √121 = 0 II: y2- 121 = 0 The number of solutions of x2+ 4|x| + 5 = 0 is The sum of three consecutive multiples of 4 is 444. Find the products of these three multiples.

if P2+1P2=7{P^2} + {1 \over {{P^2}}} = 7P2+P21​=7 , then find the value of P2−1P2.{P^2} - {1 \over {{P^2}}}.P2−P21​.Reading

if P2+1P2=7{P^2} + {1 \over {{P^2}}} = 7P2+P21​=7 , then find the value of P2−1P2.{P^2} - {1 \over {{P^2}}}.P2−P21​.

Explanation

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if ${P^2} + {1 \over {{P^2}}} = 7$ , then find the value of ${P^2} - {1 \over {{P^2}}}.$
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if ${P^2} + {1 \over {{P^2}}} = 7$ , then find the value of ${P^2} - {1 \over {{P^2}}}.$