Question

A square + 1 upon a square is equal to 7 find a square minus one upon a square

Answer 1

Answer:

Value of a square minus one upon a square is √45

Step-by-step explanation:

It is given that the value of "a square + 1 upon a square is 7",

Mathematically,

$\implies a^2+\dfrac{1}{a^2}=7$

According to the question : -

= > a^2 + 1 / a^2 = 7

Square on both sides,

= > a^4 + 1 / a^4 + 2 = 49

= > a^4 + 1 / a^4 = 49 - 2

Subtract 2 from both sides,

= > a^4 + 1 / a^4 - 2 = 47 - 2

= > a^4 + 1 / a^4 - 2( x^2 × 1 / x^2 ) = 45

= > ( a^2 - 1 / a^2 )^2 = 45

= > a^2 - 1 / a^2 = √45

Hence, value of a^2 - 1 / a^2 is √45.

Answer 2

a^2 +1/a^2 =7
(a+1/a)^2 - 2=7
a+1/a=3
(a-1/a)^2 +2=7
a-1/a=v5
a^2 - 1/a^2 =3v5