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If x^2+a^2=y^2+b^2=ax+by=1 , find the numeric vale of a^2+b^2.

Malyarpita Singh , 6 Years ago
Grade 10
anser 1 Answers
Samyak Jain

Last Activity: 6 Years ago

x2 + a2 = 1              ….............(1)
y2 + b2 = 1              ….............(2)
ax + by = 1             ….............(3)
In (1), x will take that value that makes x2 + a2 = 1.
So let x = a. This implies 2a2 = 1  i.e. a = \pm1/\sqrt{}2 = x
a = \pm1/\sqrt{}2 = x satisfies (1). So our assumption is correct.
Similarly taking y = b, we get b = \pm1/\sqrt{}2 = y, which satisfies (2).
Now, x = y = a = b = \pm1/\sqrt{}2 , which satisfies (3) also.
Hence, a2 + b2  =  (\pm1/\sqrt{}2)2  +  (\pm1/\sqrt{}2)2
                          = ½  + ½ 
                          =  1

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