If (a=3-√5/3+√5),(b=3+√5/3-√5). Find the value of (a^2+b^2).
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Step-by-step explanation:
a=3-√5/3+√5
a=3-√5(3-√5)/(3)²-(√5)²
a=9-3√5-3√5+5/9-5
a=14-6√5/4
b=3+√5/3-√5
b=3+√5(3+√5)/(3)²-(√5)²
b=9+3√5+3√5+5/9-5
b=14+6√5/4
a²-b²=(a+b)(a-b)
=(14-6√5/4+14+6√5/4)(14-6√5/4-14+6√5/4)
=(14-6√5+14+6√5/4)(14-6√5-14+6√5/4)
=28/4*0/4
=7*0
=0
therefore the value is 0
hope it helps
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